The ratio of θ-congruent numbers

Details The ratio of θ-congruent numbers The ratio of θ-congruent numbers

2010-05-31

arxiv.org/abs/1005.5579v1

Mathematics

Number Theory

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

Scientific paper

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.

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