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  • 1 Neijiang Normal University Department of Mathematics Key Laboratory of Numerical Simulation of Sichuan Province Neijiang Sichuan 641112 P. R. China
  • 2 Purdue University North Central Department of Mathematics 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 = 144k3 + 192k2 + 76k + 8.