Dujella, Andrej, Kolokvij marec 2014

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In this talk, we survey classical and recent results on Diophantine m-tuples, i.e. sets of non-zero integers (or rationals) with the property that product of any two of its distinct elements is one less then a perfect square. We will describe connections of this problem with systems of Pellian equations and with elliptic curves. We also consider several generalizations of this notion, in particular those where perfect squares are replaced by perfect powers.

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