AbstractWe give the complete solutions to the diophantine equation X+Y+Z=W in coprime positive integers X, Y, Z, W such that each of the numbers X, Y, Z, W has prime factors 2 and 3 only. The solution with the largest value of W is 2333 + 29 + 1= 36. The method works for any pair of primes (p, q) in place of (2, 3)
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They pr...
AbstractWe give the complete solutions to the diophantine equation X+Y+Z=W in coprime positive integ...
AbstractBy Theorems 1, 2 and 3 it becomes a simple matter to solve any equation px−qy=n,pxqy±pz±qw±1...
summary:In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the t...
In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y...
Let $c$ be a positive odd integer and $R$ a set of $n$ primes coprime with $c$. We consider equation...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
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...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
We show that the Diophantine equation 2x+ 17y = z^2, has exactlyve solutions (x; y; z) in positive i...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They pr...
AbstractWe give the complete solutions to the diophantine equation X+Y+Z=W in coprime positive integ...
AbstractBy Theorems 1, 2 and 3 it becomes a simple matter to solve any equation px−qy=n,pxqy±pz±qw±1...
summary:In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the t...
In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y...
Let $c$ be a positive odd integer and $R$ a set of $n$ primes coprime with $c$. We consider equation...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
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...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
We show that the Diophantine equation 2x+ 17y = z^2, has exactlyve solutions (x; y; z) in positive i...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They pr...
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