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On θ-congruent numbers on real quadratic number fields

On θ-congruent numbers on real quadratic number fields

Let K = Q ( $\sqrt{m}$) be a real quadratic number field, where m > 1 is a squarefree integer. Suppose that 0 < θ < π has rational cosine, say cos(θ) = s/r with 0 < | s| < r and gcd( r,s) = 1. A positive integer n …