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Mathematics > Number Theory

Title: Rational Diophantine sextuples with strong pair

Abstract: A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that $a_i a_j+1$ is a perfect square for all $1\le i <j \le m$, is called a rational Diophantine $m$-tuple. If in addition, $a_i^2+1$ is a perfect square for $1\le i\le m$, then we say the $m$-tuple is strong. In this paper, we construct infinite families of rational Diophantine sextuples containing a strong Diophantine pair.
Comments: 9 pages
Subjects: Number Theory (math.NT)
Cite as: arXiv:2403.17959 [math.NT]
  (or arXiv:2403.17959v1 [math.NT] for this version)

Submission history

From: Matija Kazalicki [view email]
[v1] Tue, 12 Mar 2024 23:43:02 GMT (10kb)

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