The ratio of \theta-congruent numbers
Number Theory
2010-06-01 v1 Algebraic Geometry
Abstract
Let 0<\theta<\pi such that \cos\theta\in \Q. In this paper, we prove that for given positive square-free coprime integers k,l, there exist infinitely many pairs (M,N) of \theta-congruent numbers such that lN=kM. This generalize the previous result of Rajan and Ramaroson [A. Rajan and F. Ramaroson, Ratios of congruent numbers, Acta Arithemetica 128 (2007), no. 2, 101-106] on the ratio of congruent numbers from congruent numbers (i.e. \theta=\pi/2) to arbitrary \theta-congruent numbers.
Keywords
Cite
@article{arxiv.1005.5579,
title = {The ratio of \theta-congruent numbers},
author = {Yan Li and Su Hu},
journal= {arXiv preprint arXiv:1005.5579},
year = {2010}
}
Comments
10 pages, Mathematica 7.0 is used to get the results in this paper