engleski

On the number of Diophantine m-tuples

A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine m-tuples for m = 2, 3 and 4. In this paper, we derive asymptotic extimates for the number of Diophantine pairs, triples and quadruples with elements less than given positive integer N.

Diophantine m-tuples; order of magnitude

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