Abstract
We prove that for integers a > b > c > 0 a>b>c>0 , the greatest prime factor of ( a b + 1 ) ( a c + 1 ) (ab+1)(ac+1) tends to infinity with a a . In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product ( a b + 1 ) ( a c + 1 ) ( b c + 1 ) (ab+1)(ac+1)(bc+1) .
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