Abstract
Given a finite set of primes S and an m-tuple (a1, …, am) of positive, distinct integers we call the m-tuple S-Diophantine, if for each 1 ≤ i < j ≤ m the quantity aiaj + 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 .