D(n)-quintuples with square elements
Abstract
For an integer n, a set of m distinct nonzero integers a1,a2,...,am such that ai aj+n is a perfect square for all 0<i<j<m+1, is called a D(n)-m-tuple. In this paper, we show that there are infinitely many essentially different D(n)-quintuples with square elements. We obtained this result by constructing genus one curves on a certain double cover of A2 branched along four curves.
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