ON THE GREATEST PRIME FACTOR OF (ab+ 1)(ac+ 1)

@inproceedings{Corvaja2003ONTG,
  title={ON THE GREATEST PRIME FACTOR OF (ab+ 1)(ac+ 1)},
  author={Pietro Corvaja and Umberto Zannier},
  year={2003}
}
We prove that for integers a > b > c > 0, the greatest prime factor of (ab+1)(ac+1) tends to infinity with a. In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product (ab + 1)(ac + 1)(bc + 1). In the paper [GSS], Gÿory, Sarkozy and Stewart conjectured that, for positive integers a > b > c, the greatest prime factor of the product (ab+ 1)(ac+ 1)(bc+ 1) tends to infinity as a → ∞. In the direction of this conjecture, some… CONTINUE READING
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