engleski

Diophantine m-tuples for linear polynomials. II. Equal degrees

In this paper we prove the best possible upper bounds for the number of elements in a set of polynomials with integer coefficients all having the same degree, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. Moreover, we prove that there does not exist a set of more than 12 polynomials with integer coefficients and with the property from above. This significantly improves a recent result of the first two authors with R. F. Tichy.

diophantine m-tuples; linear polynomials; Mason's inequality

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