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A set of m positive integers {a 1 , a 2 , . . . , am} is called a Diophantine m-tuple if a i a j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In [16] Dujella proved that there is no Diophantine sextuple and that there are at most finitely many Diophantine quintuples. In particular, a folklore conjecture concerning Diophantine m-tuples states that no Diophantine quintuple exists at all. In this paper we prove this conjecture.

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Bing He

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There is no Diophantine quintuple

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