A note on the number of S-Diophantine quadruples

2014/03/07 by Luca, Florian, Ziegler, Volker
#11D45 #11N32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.1674

Abstract

Let (a₁,…, a_m) be an m-tuple of positive, pairwise distinct, integers. If for all 1≤ i< j ≤ m the prime divisors of a_ia_j+1 come from the same fixed set S, then we call the m-tuple S-Diophantine. In this note we estimate the number of S-Diophantine quadruples in terms of |S|=r.

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