On sums of triangular numbers

Abstract

We study decompositions of natural numbers into triangular summands. For instance, we prove that any natural number can be represented as a sum of four triangular numbers, two of them having even indices and the other two having odd indices. This settles a conjecture by Zhi-Wei Sun (arXiv:1503.03743v8).

References in corpus (1)

• A result similar to Lagrange's theorem

Cited by in corpus (1)

• Sums of four polygonal numbers with coefficients