engleski

On a family of two-parametric D(4)-triples

Let k be a positive integer. In this paper, we study a parametric family of the sets of integers {; ; k, A2k + 4A, (A + 1)2k + 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 = (A^4 + 2A^3 + A^2)k^3 + (8A^3 + 12^A2 + 4A)k^2 +(20A^2 + 20A + 4)k + (16A + 8) for 1 <= A <= 22 and A >= 51767.

Diophantine m-tuples; Pell equations; Baker's method.

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