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)
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
Suppose that $U_n$ is a Lucas sequence of first kind and has a dominant root $\alpha$ with $\alpha>1...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
In this paper, we present a simple and fast method for counting the number of nonnegative integer so...
Abstract|In this paper, we present a simple and fast method for counting the number of nonnegative i...
We study solvability of the Diophantine equation in integers satisfying the conditions and for . The...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points o...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
We define a computable function f from positive integers to positive integers. We formulate a hypoth...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
Suppose that $U_n$ is a Lucas sequence of first kind and has a dominant root $\alpha$ with $\alpha>1...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
AbstractLet A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
In this paper, we present a simple and fast method for counting the number of nonnegative integer so...
Abstract|In this paper, we present a simple and fast method for counting the number of nonnegative i...
We study solvability of the Diophantine equation in integers satisfying the conditions and for . The...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points o...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
We define a computable function f from positive integers to positive integers. We formulate a hypoth...
Komatsu† Abstract. We determine the number of solutions of the equation a1x1+a2x2+ · · ·+amxm = b i...
Suppose that $U_n$ is a Lucas sequence of first kind and has a dominant root $\alpha$ with $\alpha>1...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
DOI
Add to ORKG