AbstractIn this paper we solve x3 + y + 1 − xyz = 0 completely and study a pair of simultaneous cubic diophantine equations (1) x | y3 + 1 and y | x3 + 1, where x and y are positive integers. The main result in this paper is that there exist an infinite number of sequences such that x and y satisfy (1) if and only if they are consecutive terms of one of these sequences
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
AbstractIn this paper we solve x3 + y + 1 − xyz = 0 completely and study a pair of simultaneous cubi...
AbstractWe prove that the equation x2 − kxy + y2 + x = 0 with k ϵ N+ has an infinite number of posit...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
In this paper, we consider the problem about finding out perfect powers in an alternating sum of con...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
AbstractIn this paper, we show that if (un)n⩾1 is a Lucas sequence, then the Diophantine equation un...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
AbstractThe solutions to a certain system of Diophantine equations and congruences determine, and ar...
In this paper, we show that if (u<SUB>n</SUB>)<SUB>n≥1</SUB> is a Lucas sequence, then the Diophanti...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
AbstractIn this paper we solve x3 + y + 1 − xyz = 0 completely and study a pair of simultaneous cubi...
AbstractWe prove that the equation x2 − kxy + y2 + x = 0 with k ϵ N+ has an infinite number of posit...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
In this paper, we consider the problem about finding out perfect powers in an alternating sum of con...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
AbstractIn this paper, we show that if (un)n⩾1 is a Lucas sequence, then the Diophantine equation un...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
AbstractThe solutions to a certain system of Diophantine equations and congruences determine, and ar...
In this paper, we show that if (u<SUB>n</SUB>)<SUB>n≥1</SUB> is a Lucas sequence, then the Diophanti...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
DOI
Add to ORKG