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Original scientific paper

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

Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia
Bo He ; Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan, 623000, P. R. China
Alain Togbé orcid id ; Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA

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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= (A4 + 2A3 + A2)k3 + (8A3 + 12A2 + 4A)k2 + (20A2 + 20A + 4) k + (16A + 8)
for 1≤ A ≤22 and A ≥ 51767.


Diophantine m-tuples, Pell equations, Baker's method

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