Add to ORKGAbstract. Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX2 bY 4 = , where 2 f1; 2;4g. Recently, these results have been improved using a number of methods. Remarkably, the equation aX2 bY 4 = 2 remains elusive, as there have been no results in the literature which are comparable to results proved for the other values of . In this paper we give a sharp estimate for the number of integer solutions in the particular case that a = 1 and b is of a certain form. As a consequence of this result, we give an elementary solution to a Diophantine problem due to Martin Gardner which was previously solved by Charles Grinstead using Baker's theory. 1
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX^2 - bY^4 = δ, where δ...
Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX^2 - bY^4 = δ, where δ...
Using the Thue-Siegel method, it is eectively proved that for an odd positive integer t, there are a...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
Using a classical result of Thue, we give an upper bound for the number of solutions to a family of ...
If the quaternary quartic equation 9 · (u² + 7v²)² − 7 · (r² + 7s²)² = 2 (*) which M. Davis put...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
Abstract. A particular case of a conjecture of Erdös and Graham, which concerns the number of integ...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX^2 - bY^4 = δ, where δ...
Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX^2 - bY^4 = δ, where δ...
Using the Thue-Siegel method, it is eectively proved that for an odd positive integer t, there are a...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
Using a classical result of Thue, we give an upper bound for the number of solutions to a family of ...
If the quaternary quartic equation 9 · (u² + 7v²)² − 7 · (r² + 7s²)² = 2 (*) which M. Davis put...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
Abstract. A particular case of a conjecture of Erdös and Graham, which concerns the number of integ...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...