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arXiv · 2001.10702

Doubly regular Diophantine quadruples

Andrej Dujella·Vinko Petričević
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Abstract

For a nonzero integer n, a set of m 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 D(n)-m-tuple. In this paper, by using properties of so-called regular Diophantine m-tuples and certain family of elliptic curves, we show that there are infinitely many essentially different sets consisting of perfect squares which are simultaneously D(n_1)-quadruples and D(n_2)-quadruples with distinct non-zero squares n_1 and n_2.

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BibTeXRIS

Andrej Dujella, Vinko Petričević. 2020-01-29. Doubly regular Diophantine quadruples. https://doi.org/10.1007/s13398-020-00921-4

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