Original scientific paper

Any polynomial D(4) - quadruple is regular

Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Yasutsugu Fujita ; Mathematical Institute, Tohoku University, Sendai, Japan

Abstract

In this paper we prove that if {a,b,c,d} is a set of four non-zero polynomials with integer coefficients, not all constant, such that the product of any two of its distinct elements increased by $4$ is a square of a polynomial with integer coefficients, then (a+b-c-d)^2=(ab+4)(cd+4).

Keywords

Diophantine m-tuples; polynomial Pellian equations

Hrčak ID:

23556

URI

https://hrcak.srce.hr/23556

Publication date:

28.5.2008.

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