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关于指数丢番图方程的Hugh Edgar问题

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哈尔滨工业大学学报 1986年第3期 112-113页

作者：曹珍富哈尔滨工业大学应用数学系

p;=q;+2 m>1, n>1 （1）where p and q are primes, has the solution 3;=5;+*** asked a question how many solutions else are there? Later, Hugh Edgar asked another question how many solutions（m,n） does the diophantine equation p;-q;=2;;m>1,n≥1,（2） have for primes p, q and integer h? In the references at el., Hall’s and Hugh Edgar’s problems were partly solved. In this paper, we have proved the following results: THEOREM 1. If p=qt;±4 or q=pt;±4, then the equation p;-q;=4 has no integer solution in which m>1, n>1. THEOREM 2. If（p,q）=（3,5）, （5,3）, （5,7）, （7,5）(mod 8), then Eq.（2） has no integer solution in which h≥2, except that 3;-5;=2;, 5;-11;=2;and

关键词： exponential diophantine equation difference of two powers. The diophantine equation

Non-Negative Integer Solutions of Two diophantine equations 2^x + 9^y = z² and 5^x + 9^y = z²

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Journal of Applied Mathematics and Physics 2016年第4期4卷 762-765页

作者： Md. Al-Amin Khan Abdur Rashid Md. Sharif Uddin Department of Mathematics Jahangirnagar University Dhaka Bangladesh

In this paper, we study two diophantine equations of the type px + 9y = z2 , where p is a prime number. We find that the equation 2x + 9y = z2 has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, ... 详细信息

关键词： exponential diophantine equation Integer Solutions

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关于丢番图方程ax2+by2=pz

哈尔滨工业大学学报 1991年第6期 108-111页

作者：曹珍富哈尔滨工业大学数学系

0 Introduction Let p be a prime, and let a, b∈Z>0, a>b>1 and （a, b）=1. If the equation X2+abY2=pz, （X,Y）=1, Z>0 （1） has an integer solution （X,Y, Z）, then there exists a unique integer solution （Xp, Yp, Zp,）which satisfies Xp>0, Yp>0 and Zpp, Yp, Zp） is called the least solution of （1）. In this paper, we prove the following results. Theorem 1 If x, y∈Z>0satisfy the equation ax2+by2=2z,z>2 （2） and x|*a, y|*b, where symbol x|*a means that a is divided exactly by each prime factor of x.

关键词： exponential diophantine equation Hugh Edgar’s problem

A Kind of diophantine equations in Finite Simple Groups

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Northeastern Mathematical Journal 2000年第4期16卷 391-397页

作者：曹珍富 Harbin Institute of Technology

In this paper, we prove that if p, q are distinct primes, (p,q)≡(1,7) (mod 12) and Legendres symbol pq=1 , then the equation 1+p a=2 bq c+2 dp eq f has only solutions of the form (a,b,c,d,e,f)=(t,0,0,0,t,0), where t is a non negative integer. We also give all solutions of a kind of generalized Ramanujan Nagell equations by using the theories of imaginary quadratic field and Pells equation.

关键词： exponential diophantine equation generalized Ramanujan Nagell equation finite simple group difference set

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