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 e-prints
- 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
- E-Print:
- 11 pages