On the family of diophantine triples {<Emphasis Type="Italic">k</Emphasis> + 1, 4<Emphasis Type="Italic">k</Emphasis>, 9<Emphasis Type="Italic">k</Emphasis> + 3} |
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| Authors: | Bo He Alain Togbé |
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| Institution: | (1) Department of Mathematics Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, 641112, P. R. China;(2) Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN 46391, USA |
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| 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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| Keywords: | and phrases" target="_blank"> and phrases Diophantine m-tuple Pell equation Diophantine approximation linear forms in logarithms |
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