Abstract
Let A and k be positive integers. We study the Diophantine quadruples
. We prove that if d is a positive integer such that the product of any two distinct elements of the set increased by 1 is a perfect square, then
when 3 ≦ A ≦ 10. This extends a theorem obtained by Dujella [7] for A = 1, and also, a classical theorem of Baker and Davenport [2] for A = k = 1.
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The first author is supported by the Foundation of Key Laboratory of Numerical Simulation of Sichuan Province. The second author is partially supported by Purdue University North Central.
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He, B., Togbé, A. On a family of diophantine triples {k, A 2 k + 2A, (A + 1)2 k + 2 (A + 1)} with two parameters. Acta Math Hung 124, 99–113 (2009). https://doi.org/10.1007/s10474-009-8155-5
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DOI: https://doi.org/10.1007/s10474-009-8155-5