Finding all S-Diophantine quadruples for a fixed set of primes S

2020/10/22 by Ziegler, Volker
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.11670

Abstract

Given a finite set of primes S and a m-tuple (a₁,…,a_m) of positive, distinct integers we call the m-tuple S-Diophantine, if for each 1≤ i < j≤ m the quantity a_ia_j+1 has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find all S-Diophantine quadruples, provided that |S|=3.

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