Browsing by Subject "Gallagher's sieve"

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    The Paley graph conjecture and Diophantine m-tuples
    (Elsevier, 2020) Güloğlu, Ahmet M.; Murty, M. R.
    A Diophantine m-tuple with property D(n), where n is a nonzero integer, is a set of m positive integers {a1, ..., am} such that aiaj + n is a perfect square for all 1 i < j m. It is known that Mn = sup{|S| : S is a D(n) m-tuple} exists and is O(log |n|). In this paper, we show that the Paley graph conjecture implies that the upper bound can be improved to (log |n|), for any > 0.