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The extension of the $D(-k)$-pair $\{k,k+1\}$ to a quadruple

Published 13 Jan 2020 in math.NT | (2001.04160v1)

Abstract: Let $k$ be a positive integer. In this paper, we prove that if ${k,k+1,c,d}$ is a $D(-k)$-quadruple with $c>1$, then $d=1$.

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