AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of integer solutions (x1, …, xr) satisfying the Diophantine equation ∑j=1rAjxj = A and the conditions 0 ⩽ xi ⩽ xj, j = 1, …, r. This paper expresses f(A) recursively as a linear function of f(0), f(1), …, f(A−1)
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
We study the Diophantine equation xm−1 x−1 = yn−1 y−1 in integers x > 1, y > 1, m > 1, n &g...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
Abstract|In this paper, we present a simple and fast method for counting the number of nonnegative i...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
AbstractFor a class of strictly increasing real valued functions f(n) we obtain an upper bound for t...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
Abstract. In this paper, we prove a weaker form of a conjecture of Mohanty and Ramasamy [6] concerni...
SIGLETIB: RN 4020 (774) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbi...
The paper solves a previously posed problem by proving a certain uniform bound for the number of so...
For any positive integer n, let f(n) denote the number of solutions to the Diophantine equation 4
Let t ≥ 2 be a positive integer. Extending the work of A. Tekcan, here we consider the number of int...
AbstractLet m and n be positive integers and p any odd prime. In this paper we consider the Diophant...
Let D1 and D2 be coprime positive integers and let k be an odd positive integer coprime with D1D2. W...
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
We study the Diophantine equation xm−1 x−1 = yn−1 y−1 in integers x > 1, y > 1, m > 1, n &g...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
Abstract|In this paper, we present a simple and fast method for counting the number of nonnegative i...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
AbstractFor a class of strictly increasing real valued functions f(n) we obtain an upper bound for t...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
Abstract. In this paper, we prove a weaker form of a conjecture of Mohanty and Ramasamy [6] concerni...
SIGLETIB: RN 4020 (774) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbi...
The paper solves a previously posed problem by proving a certain uniform bound for the number of so...
For any positive integer n, let f(n) denote the number of solutions to the Diophantine equation 4
Let t ≥ 2 be a positive integer. Extending the work of A. Tekcan, here we consider the number of int...
AbstractLet m and n be positive integers and p any odd prime. In this paper we consider the Diophant...
Let D1 and D2 be coprime positive integers and let k be an odd positive integer coprime with D1D2. W...
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
We study the Diophantine equation xm−1 x−1 = yn−1 y−1 in integers x > 1, y > 1, m > 1, n &g...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
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