Mixed sums of squares and triangular numbers
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505128
 arXiv:
 arXiv:math/0505128
 Bibcode:
 2005math......5128S
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics;
 11E25;
 05A30;
 11B65;
 11D85;
 11P99
 EPrint:
 11 pages