The ratio of θ-congruent numbers

Abstract

Let 0<θ<πsuch that \cosθ\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 θ-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. θ=π/2) to arbitrary θ-congruent numbers.

10 pages, Mathematica 7.0 is used to get the results in this paper