engleski

Diophantine quadruples with the properties D(n1) and D(n2)

For a nonzero integer n, a set of m distinct nonzero integers {; ; ; ; ; ; a1, a2, ..., am}; ; ; ; ; ; such that aiaj + n is a perfect square for all 1 ≤ i < j ≤ m, is called a D(n)-m-tuple. In this paper, we show that there infinitely many essentially different quadruples which are simultaneously D(n1)-quadruples and D(n2)-quadruples with n1 ̸= n2.

Diophantine quadruples, elliptic curves

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