Güloğlu, Ahmet M.Murty, M. R.2021-02-242021-02-2420200097-3165http://hdl.handle.net/11693/75560A 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.EnglishDiophantine m-tuplesGallagher's sieveVinogradov's inequalityPaley graph conjectureArticle10.1016/j.jcta.2019.105155