Mixed sums of squares and triangular numbers

Details Mixed sums of squares and triangular numbers Mixed sums of squares and triangular numbers

2005-05-09

arxiv.org/abs/math/0505128v9

Acta Arith. 127(2007), no.2, 103-113

Mathematics

Number Theory

11 pages

Scientific paper

By means of $q$-series, we prove that any natural number is a sum of an even
square and two triangular numbers, and that each positive integer is a sum of a
triangular number plus $x^2+y^2$ for some integers $x$ and $y$ with
$x\not\equiv y (mod 2)$ or $x=y>0$. The paper also contains some other results
and open conjectures on mixed sums of squares and triangular numbers.

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