On prime factors of integers of the form (ab+1)(bc+1)(ca+1)

Volume 79 / 1997

K. Győry, A. Sárközy Acta Arithmetica 79 (1997), 163-171 DOI: 10.4064/aa-79-2-163-171


1. Introduction. For any integer n > 1 let P(n) denote the greatest prime factor of n. Győry, Sárközy and Stewart [5] conjectured that if a, b and c are pairwise distinct positive integers then (1) P((ab+1)(bc+1)(ca+1)) tends to infinity as max(a,b,c) → ∞. In this paper we confirm this conjecture in the special case when at least one of the numbers a, b, c, a/b, b/c, c/a has bounded prime factors. We prove our result in a quantitative form by showing that if


  • K. Győry
  • A. Sárközy

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