engleski

On Diophantine m-tuples and D(n)-sets

For a nonzero integer n, a set of distinct nonzero integers {; ; ; ; ; ; a 1 , a 2 , . .. , a m }; ; ; ; ; ; such that a i a j + n is a perfect square for all 1 ≤ i < j ≤ m, is called a Diophantine m- tuple with the property D(n) or simply D(n)- set. Such sets have been studied since the ancient times. In this article, we give an overview of the results from the literature about D(n)-sets and summarize our recent findings about triples of integers which are D(n)-sets for several n's. Furthermore, we include some new observations and remarks about the ways to construct such triples.

Diophantine m-tuples, elliptic curves

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