Let rk(n) and tk(n) denote the number of representations of n as a sum of k squares, and as a sum of k triangular numbers, respectively. We give a generalization of the result rk(8n + k) = cktk(n), which holds for 1 ≤ k ≤ 7, where ck is a constant that depends only on k. Two proofs are provided. One involves generating functions and the other is combinatorial
Abstract. Let t(n) be the number of representations of n as a sum of three triangles. We prove infin...
In this paper, we present eighteen interesting infinite products and their Lambert series expansions...
Let k and n be positive integers. Let sk(n) denote the number of representations of n as the sum of ...
Let rk(n) denote the number of representations of n as a sum of k squares and tk(n) the number of re...
AbstractWith rk(n) denoting the number of representations of n as the sum of k squares and tk(n) the...
AbstractWith rk(n) denoting the number of representations of n as the sum of k squares and tk(n) the...
Let ck(m) denote the number of representations of integer m as a sum of k cubes and pk(m) denote the...
In this study, we seek to find relations between the number of representations of a nonnegative int...
Let Ф (m, k)(n) denote the number of representations of an integer n as a sum of k 2mth powers and Ψ...
of all integers, and Q the set of all rational numbers. For n 2 N [ f0g and k 2 N we let rk(n) denot...
The triangular numbers are the integers m(m + 1)/2, m = 0, 1, 2, . . . . For a positive integer k, w...
Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. In...
For positive Integers 11 and k, we * let ~ ( n) denote the number of representations of rt as the ...
Abstract. We give a variety of results involving s(n), the number of representations of n as a sum o...
Let $ r_k(n)$ denote the number of representations of the positive integer $ n$ as the sum of $ k$ s...
Abstract. Let t(n) be the number of representations of n as a sum of three triangles. We prove infin...
In this paper, we present eighteen interesting infinite products and their Lambert series expansions...
Let k and n be positive integers. Let sk(n) denote the number of representations of n as the sum of ...
Let rk(n) denote the number of representations of n as a sum of k squares and tk(n) the number of re...
AbstractWith rk(n) denoting the number of representations of n as the sum of k squares and tk(n) the...
AbstractWith rk(n) denoting the number of representations of n as the sum of k squares and tk(n) the...
Let ck(m) denote the number of representations of integer m as a sum of k cubes and pk(m) denote the...
In this study, we seek to find relations between the number of representations of a nonnegative int...
Let Ф (m, k)(n) denote the number of representations of an integer n as a sum of k 2mth powers and Ψ...
of all integers, and Q the set of all rational numbers. For n 2 N [ f0g and k 2 N we let rk(n) denot...
The triangular numbers are the integers m(m + 1)/2, m = 0, 1, 2, . . . . For a positive integer k, w...
Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. In...
For positive Integers 11 and k, we * let ~ ( n) denote the number of representations of rt as the ...
Abstract. We give a variety of results involving s(n), the number of representations of n as a sum o...
Let $ r_k(n)$ denote the number of representations of the positive integer $ n$ as the sum of $ k$ s...
Abstract. Let t(n) be the number of representations of n as a sum of three triangles. We prove infin...
In this paper, we present eighteen interesting infinite products and their Lambert series expansions...
Let k and n be positive integers. Let sk(n) denote the number of representations of n as the sum of ...
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