Geodesic
On prime factors of integers of the form (ab+1)(bc+1)(ca+1)
Acta Arithmetica, Tome 79 (1997) no. 2, pp. 163-171.

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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
DOI : 10.4064/aa-79-2-163-171

K. Győry 1 ; A. Sárközy 1

1 
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K. Győry; A. Sárközy. On prime factors of integers of the form (ab+1)(bc+1)(ca+1). Acta Arithmetica, Tome 79 (1997) no. 2, pp. 163-171. doi : 10.4064/aa-79-2-163-171. http://geodesic.mathdoc.fr/articles/10.4064/aa-79-2-163-171/

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