On the Diophantine equation pq=x²+ny²

2014/04/03 by Ja Kyung Koo, Koo, Ja Kyung, Dong Hwa Shin +1
Mathematics · #Mathematical Dynamics and Fractals #Analytic Number Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1404.1060

Abstract

Let n be a positive integer. We discuss pairs of distinct odd primes p and q not dividing n for which the Diophantine equations pq=x²+ny² have integer solutions in x and y. As its examples we classify all such pairs of p and q when n=5 and 14.

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