engleski

Diophantine D(4)-m-tuples

We call the set of m positive distinct integers D(n)-m-tuple if the product of any of its two elements increased by n is a perfect square. We will present some methods that led to the proof that D(4)-quintuple doesn’t exist and give comparison with the case n = 1. The conjecture that an extension of a D(n)- triple to a D(n)-quadruple is unique is still an open problem in both cases n = 1 and n = 4, so we will present some known properties of these quadruples. Results from this poster are from joint works with A. Filipin.

diophantine m-tuples, diophantine equations, pell equations

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