Complete solution of the polynomial version of a problem of Diophantus (CROSBI ID 105526)
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Podaci o odgovornosti
Dujella, Andrej ; Fuchs, Clemens
engleski
Complete solution of the polynomial version of a problem of Diophantus
In this paper, we prove that if {;a, b, c, d}; is a set of four non-zero polynomials with integer coeficients, not all constant, such that the product of any two of its distinct elements plus 1 is a square of a polynomial with integer coeficients, then (a + b − c − d)^2 = 4(ab + 1)(cd + 1). This settles the strong Diophantine quintuple conjecture for polynomials with integer coeficients.
Diophantine m-tuples; simulatenous Pellian equation; linear recurring sequences
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