On a Family of Two-parametric D(4)-triples
نویسندگان
چکیده
Let k be a positive integer. In this paper, we study a parametric family of the sets of integers {k, Ak + 4A, (A+ 1)k + 4(A+ 1), d}. We prove that if d is a positive integer such that the product of any two distinct elements of that set increased by 4 is a perfect square, then d = (A4 + 2A3 +A2)k3 + (8A3 + 12A2 + 4A)k2 +(20A2 + 20A + 4)k + (16A+ 8) for 1 ≤ A ≤ 22 and A ≥ 51767.
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