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Fermat and Pythagoras Divisors for a New Explicit Proof of Fermat’s Theorem:a⁴ + b⁴ = c⁴. Part I

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Advances in Pure Mathematics 2024年第4期14卷 303-319页

作者： Prosper kouadio Kimou François Emmanuel Tanoé Kouassi Vincent kouakou Laboratoire d’ Informatique et de Math&#233matiques appliqu&#233es Institut Polytechnique F&#233lix Houphou&#235t BOIGNY Yamoussoukro Cote d&#8217Ivoire UFR Mathé matiques et Informatique Universit&#233 F&#233lix Houphouet BOIGNY Abidjan Cote d&#8217Ivoire UFR Sciences Fondamentales Appliqué es Universit&#233 NANGUI ABROGOUA Abidjan Cote d&#8217Ivoire

In this paper we prove in a new way, the well known result, that Fermat’s equation a4 + b4 = c4, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (Fb>0b>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1bsurd. To reach such a result, we suppose first that (Fb>0b>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (Fb>0b>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s b 2 d b , where ( 2 s b 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=

关键词： Factorisation in ℤ Greatest Common Divisor Pythagoras Equation Pythagorician Triplets Fermat's Equations Pythagorician Divisors Fermat's Divisors Diophantine Equations of Degree 2 4-Integral Closure of ℤ in ℚ

Detection of burned Areas through Spectral Indices Analysis of Sentinel-2A Satellite Images in the Abokouamékro Wildlife Reserve (Central, Côte D’Ivoire)

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Open Journal of Applied Sciences 2024年第1期14卷 205-222页

作者： b.b.kouakou kouadio Sié Ouattara Alain Clément Jean-Marc Gala bi Zaouri Jean-Luc kouadio Kouassi Jean-Luc Edouard kouakou N’guessan Laboratoire des Sciences et Technologies de la Communication et de l’Information (LSTCI) Institut National Polytechnique Houphou&#235t Boigny (INP-HB) Yamoussoukro C&#244te d’Ivoire Laboratoire des Sciences Agronomiques et Génie Rural Institut National Polytechnique Houphou&#235t Boigny (INPHB) Yamoussoukro C&#244te d’Ivoire Ecole de Géomatique et du Territoire (EGT) Abidjan C&#244te d’Ivoire LARIS SFR MATHSTIC Université d’Angers Angers France Centre Universitaire de Recherche et d’application en Télédétection (CURAT) UFR des Sciences de la Terre et des Ressources Minières Abidjan C&#244te d’Ivoire Laboratoire de botanique UFR Biosciences Université Félix Houphou&#235t Boigny Abidjan C&#244te d’Ivoire

In Côte d’Ivoire, the recurring and unregulated use of bushfires, which cause ecological damage, presents a pressing concern for the custodians of protected areas. This study aims to enhance our comprehension of the dynamics of burnt areas within the Abokouamékro Wildlife Reserve (AWR) by employing the analysis of spectral indices derived from satellite imagery. The research methodology began with the calculation of mean indices and their corresponding spectral sub-indices, including NDVI, SAVI, NDWI, NDMI, bAI, NbR, TCW, TCG, and TCb, utilizing data from the Sentinel-2A satellite image dated January 17, 2022. Subsequently, a fuzzy classification model was applied to these various indices and sub-indices, guided by the degree of membership α, with the goal of effectively distinguishing between burned and unburned areas. Following the classification, the accuracies of the classified indices and sub-indices were validated using the coordinates of 100 data points collected within the AWR through GPS technology. The results revealed that the overall accuracy of all indices and sub-indices declines as the degree of membership α decreases from 1 to 0. Among the mean spectral indices, NDVI-mean, SAVI-mean, NDMI-mean exhibited the highest overall accuracies, achieving 97%, 95%, and 90%, respectively. These results closely mirrored those obtained by sub-indices using band 8 (NDVI-b8, SAVI-b8, and NDMI-b8), which yield respective overall accuracies of 93%, 92%, and 89%. At a degree of membership α = 1, the estimated burned areas for the most effective indices encompassed 2144.38 hectares for NDVI-mean, 1932.14 hectares for mean SAVI-mean, and 4947.13 hectares for mean NDMI-mean. A prospective approach involving the amalgamation of these three indices could have the potential to yield improved outcomes. This study could be a substantial contribution to the discrimination of bushfires in Côte d’Ivoire.

关键词： Spectral Indices Wildfire burned Areas Abokouamékro Wildlife Reserve Côte D’Ivoire

Assessment of the Drafting Quality of Request Forms Submitted to the Malaria and Parasitology Units at the Institut Pasteur de Cote d’Ivoire

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Journal of biosciences and Medicines 2024年第5期12卷 330-339页

作者： Yao Serge-Stéphane Ako Ako bérenger Aristide Sylvain beourou Ouattara Yacouba N’Guessan Tiacoh Landry N’Dri kouadio Thierry-borel Toure André Offianan Malaria Unit Institut Pasteur de Cote d&#8217Ivoire Abidjan Cote d&#8217Ivoire Parasitology Unit Institut Pasteur de Cote d&#8217Ivoire Abidjan Cote d&#8217Ivoire

biological tests provide information on the medical analysis requested by both the patient and the prescriber. It is a communication link between the prescriber and the laboratory staff. The lack of some information on request forms not only affects the drafting quality of the test and patient care, but could also make thousands of data produced by healthcare centers unusable. The aim of this study was to assess the drafting quality of request forms submitted to the Malaria and Parasitology Units at the Institut Pasteur de Côte d’Ivoire. Methods: It was a descriptive cross-sectional study to assess the drafting quality of request forms of various prescribers received at the Institut Pasteur de Côte d’Ivoire. This study was conducted at the Malaria and Parasitology Units, department of Parasitology and Mycology (Institut Pasteur de Côte d’Ivoire), from 6th December 2020 to 6th December 2021. The information on each request forms was recorded on a data collection form designed for this purpose. Each data collection form corresponds to a request forms and each test to a patient. Results: Out of a total of 1990 request forms received, the patient’s age and sex were missing on 18% and 26.8% of the tests respectively. More than half (51.80%) of request forms did not indicate the patient’s place of residence. Clinical information was not provided on 45.90% of the tests. Prescribers omitting their signatures were 51%, stamps were 50.3% and contacts were 71.2%. Only 5.4% of request forms were of good drafting quality. Providing all the required information on the forms could facilitate the use and analysis of data and samples.

关键词： Laboratory Quality Request Forms Information

Calcium-Magnesium Ca/Mg Ratios and Their Agronomic Implications for the Optimization of Phosphate Fertilization in Rainfed Rice Farming on Acidic Ferralsol in the Forest Zone of Ivory Coast

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Open Journal of Soil Science 2024年第1期14卷 81-96页

作者： Fernand G. Yao brahima Kone Franck M. L. bahan kouadio Amani Jean L. Essehi Mamadou b. Ouattara Konan E. b. Dibi brou Kouame François Lompo Albert Yao-Kouame Central Laboratory Soils Water and Plants (LCSEP) National Center for Agronomic Research (CNRA) Bouaké Ivory Coast Soil Water and Geomaterials Sciences Laboratory (LS2EG) Cocody-Abidjan Earth Sciences and Mining Resources Training and Research Unit (UFR STRM) Félix Houphou&#235t-Boigny University Abidjan Ivory Coast Department of Rice Program Man Research Station National Center for Agronomic Research (CNRA) Man Ivory Coast Department of Geography Unit of Training and Research (UFR) Communication Environment and Society University Alassane Ouattara Bouaké Ivory Coast Food Crops Research Station (SRCV) National Agricultural Research Center (CNRA) Bouaké Ivory Coast Institute of the Environment and Agricultural Research (INERA) Ouagadougou Burkina Faso

This study is a contribution to improving rice productivity on acidic plateau soils of the tropical rainforest zone. It is based on taking into account the cationic balances of the soil in order to optimize the phosphorus (P) nutrition of rice on these acidic soils, where this nutrient constitutes a limiting factor for agricultural production. Three (3) pot trials were conducted in Adiopodoumé in the forested south of Côte d’Ivoire. The interactive effects of calcium carbonate (0, 25, 50 and 75 kg Ca ha−1) and magnesium sulfate (0, 25, 50 and 75 kg Mg ha−1) were evaluated on the response of NERICA 5 rice at doses 0, 25, 50 and 75 kg P ha−1 of natural phosphate from Togo, applied only once at the start of the experiment. Additional fertilizers of nitrogen (N) (100 kg N ha−1) and potassium (K) (50 kg KCl ha−1) were added to each of the tests in a split-plot device. The test results revealed a paddy production potential of approximately 3 to 5 t⋅ha−1 for NERICA 5 on an acidic soil, under the effect of the interaction of P, Ca and Mg. The quadratic response of rice yield to the doses of these fertilizers would be more dependent on their balance, itself influenced by Ca nutrition. For the sustainability and maintenance of rice production in agro-ecology studied, it was recommended doses of 38 kg Ca ha−1, 34 kg Mg ha−1 in a Ca/Mg ratio (1/1) with intakes of 41 kg P ha−1, overall in a ratio 1/1/1 (P/Ca/Mg) more favorable to the availability of free iron considered a guiding element of mineral nutrition. Thus, these promising results should be confirmed in a real environment for better management of the fertilization of rice cultivated on acidic plateau soils in Côte d’Ivoire.

关键词： Soil Acidity Ca/Mg Ratios Phosphate Fertilization Rice Growing Ivory Coast

Impact of Meteorological Drought on Streamflows in the Lobo River Catchment at Nibéhibé, Côte d’Ivoire

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Journal of Water Resource and Protection 2020年第6期12卷 495-511页

作者： bérenger Koffi Zilé Alex kouadio kouakou Hervé Kouassi Affoué berthe Yao Martin Sanchez kouakou Lazare Kouassi Laboratory of Science and Technology of Environment Jean Lorougnon Guédé University Daloa C&ocirc te d’Ivoire Laboratory of Planetology and Geodynamics (LPG) University of Nantes Faculty of Science and Technology Nantes France

The management of water resources in watersheds has become increasingly difficult in recent years due to the frequency and intensity of drought sequences. The Lobo River catchment, like most tropical regions, has experienced alternating wet and dry periods. These drought periods have a significant impact on the availability of water resources in the basin. The objective of this study is to analyse the impact of meteorological drought on flows in the Lobo River catchment. Therefore, using the Normalized Precipitation and Evapotranspiration Index (SPEI) and the Drought Flow Index (SDI), the characteristics of droughts were studied. The results of this study show that meteorological droughts were more frequent than hydrological droughts in the Lobo River watershed. However, the hydrological drought was longer and more intense than the meteorological drought. The greater relationship between meteorological and hydrological drought was observed at the Daloa and Vavoua station (0.43 between 2007 and 2013 in the basin. The study of these climatic trends would be very useful in the choice of management and adaptation policies for water resources management.

关键词： Rainfall Normalized Index Meteorological Drought Hydrological Drought Lobo River

Hydrochemical Characterization of Groundwater in the Sub-Prefecture of Kokumbo (Ivory Coast)

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Journal of Geoscience and Environment Protection 2023年第6期11卷 169-183页

作者： Armel kouadio Koblan Affoué bénédicte Koffi Aminata Diomandé Deh Serges kouakou Kan Jean Kouamé Jean Patrice Jourda Laboratory of Soil Water and Geomaterials Sciences (LSEG) U.F.R. Earth Sciences and Mining Resources (STRM) University of Felix Houphou&#235t-Boigny Abidjan Ivory Coast University Center for Research and Application in Remote Sensing (CURAT) University of Félix Houphou&#235t-Boigny Abidjan Ivory Coast

In the Kokumbo sub-prefecture, groundwater extraction related to gold panning remains a major concern, not to mention the deterioration of its quality. Among the work carried out on water resources, no scientific interest has been shown in groundwater to characterise it. The objective of this study is to contribute to the knowledge of its physico-chemical quality. In situ measurements and physico-chemical analyses using an inductively coupled plasma optical emission spectrometer (ICP-OES) were carried out on five (5) human-powered pump (HPP) water samples and six (6) well water samples collected during low and high water seasons. The results show that the physico-chemical quality of the water, which is sometimes turbid, is satisfactory in terms of the mineralization of the borehole and well water, and the pH of the boreholes, while the temperatures of the two waters and the pH of the wells do not comply with WHO standards. The levels of major ions are recommended for consumption. The waters are classified as predominantly bicarbonate-calcium and magnesium (73%) in the dry season and in the flood season, with an equal split between bicarbonate-calcium and magnesium (45.5%) and chloride-calcium and magnesium (45.5%). The elimination of materials responsible for the turbidity of certain waters by managers or populations is essential for drinking water use. The risk linked to this element means that these turbid waters are not recommended for drinking water.

关键词： Groundwater Physico-Chemical Parameter Hydrochemical Facies Kokumbo

Effect of Sand Partial Substitution for Glass Powder on the behaviour of Sand-Cement Mortar

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Materials Sciences and Applications 2019年第12期10卷 756-767页

作者： Séraphin Agré Djomo Conand Honoré kouakou Koffi Clément kouadio Moro Olivier boffoue Edjikémé Emeruwa Departement Sciences de la Terre UFR Environnement Universite Jean Lorougnon Guede Daloa Côte d’Ivoire Laboratoire de Géomatériaux et Technologie du bâtiment (LGTb) UFR des Sciences de la Terre et des Ressources Minières Université Felix Houphouet Boigny de Cocody Abidjan Côte d’Ivoire

Partial substitution of aggregates for pieces of glass in concrete contributes to reducing the use this resource and preserving the environment for future generations. However, concretes or mortars mixed with crushed glass can deteriorate within a few years, because of the alkali-silica reaction related to the size of glass pieces. Some investigations were carried out in order to find out how to bring down this phenomenon. Different percentages of glass powder were mixed with mortar made from sand, cement and crushed glass pieces of which diameter is between 1 and 5 mm. Products obtained were submitted to flexural testing, compressive strength testing and resistance to acid attack and Scanning Electron microscopy (SEM) observations were made after a period running from 28 to 180 days of drying. The results show an increase in the mechanical properties of products with glass powder and an improvement in the durability of mortar in acidic environment. Such improvements are related to the enhanced adhesion created between crushed glass pieces and cementitious matrix containing glass powder as a result of pozzolanic reaction.

关键词： Pozzolanic Reaction Crushed Glass Glass Powder Alkali-Silica Reaction

Acute Intestinal Invagination of the Child at the Teaching Hospital of bouaké: Ultrasound Diagnosis and Clinical-Echo-Surgical Correlation

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Open Journal of Medical Imaging 2021年第1期11卷 18-28页

作者： bouassa Davy Melaine kouakou Konaté Issa Kouamé Paul bonfils Kouassi Adoubs Cé lestin bé nié Tsri Akoli baudouin bravo Kesse Emile Tanoh Allou Florent kouadio brou Lambert Yao Achie Jean-Ré gis Akobe Sara Carole Sanogo Malick Soro kouadio N’Dri Medical Imaging and Radiodiagnostic Departement of the Teaching Hospital of bouaké Bouak&#233 Ivory Coast Training and Research Unit Medical Sciences Alassane Ouattara University Bouak&#233 Ivory Coast Pediatric Surgery Unit of the Teaching hospital of bouaké Bouak&#233 Ivory Coast

background: Acute intestinal invagination or intussusception is the most common abdominal surgical emergency in infants, but it can occur at any age. Performing an ultrasound scan at the slightest clinical suspicion contributes to early diagnosis and therapeutic management. Objective: To show the relevance of ultrasound in the therapeutic management of the child’s intussusception through a correlation between the ultrasound diagnosis and the clinical and/or per operative diagnosis. Patients and Methods: It was a retrospective study of 24 cases from July 2017 to September 2020 (30 months) in the Medical Imaging and Paediatric Surgery departments of Teaching Hospital of bouaké. We included only patients from 0 to 15 years old who had digestive symptoms, an abdominal ultrasound scan. These patients were eligible for surgery. Data analysis was performed with Epi info 7 software. Results: Median age was 17.2 months [02 - 120]. Male gender predominated (83.3%). Clinico-biological data were dominated by abdominal pain (79.2%), vomiting (75%) and rectorragies (33.3%), with Ombredanne’s triad in 33.3% and hyperleukocytosis (70.8%). Ultrasonography showed invaginated coves (95.8%) sitting in the right angl iliac fossa, peri-umbilical and right flank in 73.9%. Cockade image coupled with the sandwich image accounted for 95.6%. Superficial adenopathies (45.8%) and peri-lesional fluid effusion (20.8%) were associated with it. An occlusive syndrome complicating intussusception was observed in 41.67% associated with intra-peritoneal effusion of fluid (25%). There was a significant diagnostic agreement between the clinic, ultrasound and surgery according to the Fisher’s exact test (p = 0.002). That between ultrasound and surgery was calculated at 95.4%. Conclusion: This study allowed us to show a good clinical-echo-surgical concordance. Ultrasound is therefore an undeniable diagnostic, prognostic an

关键词： Ultrasound Acute Intestinal Invagination Child

Response of soil mite abundance and diversity to a monospecific timber Tectona grandis plantation in Ivory Coast

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Current Zoology 2013年第5期59卷 633-643页

作者： Julien kouadio N'DRI Henri Marc ANDRE Jan LAGERLOEF Jerome Ebagnerin TONDOH Thierry HANCE UFR des Sciences de la Nature/Centre de Recherche en Ecologie Universit6 d'Ab0bo-Adjam6 02 BP 801 Abidjan 02 C6te d'Ivoire Mus6e royal de l'Afrique centrale Leuvensesteenweg 13 B-3080 Tervuren Belgium Swedish University of Agricultural Sciences (SLU) Dept. of Ecology EO.Box 7044 SE-750 07 Uppsala Sweden CIAT-TSbF Institut d'Economie Rurale CRRA de Sotuba Laboratoire Sol-Eau-Plante c/o Icraf Sahel BPE 5118 Bamako Mali Universite Catholique de Louvain Biodiversity Research Center Earth and Life Institute Place Croix du Sud 4 B-1348 Lou-vain-la-Neuve Belgium

This study aims to assess the impact of monospecific Tectona grandis forest plantation on the soil mite abundance and diversity. To achieve these objectives, two sites situated in Ivory Coast were investigated. The first, a primary forest was characterized by a very weak human activities whereas the second, a teak plantation was characterized by a high disturbance performed during the planting. After extracting, sorted and description, 116 mite species were described in the two sites. Mite densities were lower in teak plantation and also higher in the litter and decreased to the depth in both sites. Species richness re- corded in teak plantation （52 species） was significantly lower compared to primary forest （98 species）. The same trend was ob- served for Oribatida but not for Gamasida. The lower Oribatida （5 vs. 17） and higher Oribatida （24 vs. 41） were recorded respec- tively in teak plantation and primary forest. Mite Shannon index and evenness were significantly different between sites. High Jaccard index values and the appearance of exclusive species in both habitats showed that the sites are very distinct. Total number of species recorded corresponded to 58%-63% of the total number of species estimated by ACE and Chao 1＆2 estimators, indi- cating that the sampling effort was not sufficient. Mite abundance and diversity varied depending on the characteristics of habi- tats. Chemical element （Corn, Ctot, Ntot, and SOM） values were lower in teak plantation （disturbed habitat） and significantly dif- ferent to primary forest in the topsoil. Apart from litter height, soil depth, pH and C/N ratio, others variables were strongly corre- lated to mite abundance and diversity [Current Zoology 59 （5）： 633-643, 2013].

关键词： Soil mite Teak plantation Diversity and community structure Disturbance.