engleski

Some Diophantine triples and quadruples for quadratic polynomials

In this paper, we give some new examples of polynomial D(n)-triples and quadruples, i.e. sets of polynomials with integer coefficients, such that the product of any two of them plus a polynomial n in Z[X] is a square of a polynomial with integer coefficients. The examples illustrate various theoretical properties and constructions for a quadratic polynomial n which appeared in recent papers. One of the examples gives a partial answer to the question about number of distinct D(n)-quadruples if n is an integer that is the product of twin primes.

Diophantine m-tuples ; polynomials

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