General relations between sums of squares and sums of triangular numbers
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Date
2004
DOI
Open Access Location
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Massey University
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Abstract
Let = ( 1, · · · , m) be a partition of k. Let r (n) denote the number of solutions in
integers of 1x21
+ · · · + mx2
m = n, and let t (n) denote the number of solutions in non
negative integers of 1x1(x1 +1)/2+· · ·+ mxm(xm +1)/2 = n. We prove that if 1 k 7,
then there is a constant c , depending only on , such that r (8n + k) = c t (n), for all
integers n.
Description
Keywords
Integers
Citation
Chandrashekar, A., Cooper, S., Han, J.H. (2004), General relations between sums of squares and sums of triangular numbers, Research Letters in the Information and Mathematical Sciences, 6, 157-161