Abstract
We prove that if k is a positive integer and d is a positive integer such that the product of any two distinct elements of the set {k + 1, 4k, 9k + 3, d} increased by 1 is a perfect square, then d = 144k 3 + 192k 2 + 76k + 8.
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Communicated by Attila Pethő
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He, B., Togbé, A. On the family of diophantine triples {k + 1, 4k, 9k + 3}. Period Math Hung 58, 59–70 (2009). https://doi.org/10.1007/s10998-009-9059-6
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DOI: https://doi.org/10.1007/s10998-009-9059-6