Representing Sets with Sums of Triangular Numbers
Abstract
We investigate here sums of triangular numbers $f(x):=\sum_i b_i T_{x_i}$ where $T_n$ is the $n$th triangular number. We show that for a set of positive integers $S$ there is a finite subset $S_0$ such that $f$ represents $S$ if and only if $f$ represents $S_0$. However, computationally determining $S_0$ is ineffective for many choices of $S$. We give an explicit and efficient algorithm to determine the set $S_0$ under certain Generalized Riemann Hypotheses, and implement the algorithm to determine $S_0$ when $S$ is the set of all odd integers.
 Publication:

arXiv eprints
 Pub Date:
 March 2009
 arXiv:
 arXiv:0903.3026
 Bibcode:
 2009arXiv0903.3026K
 Keywords:

 Mathematics  Number Theory;
 11E25
 EPrint:
 18 pages, 3 tables