engleski

Diophantine quadruples in Z[i][X]

In this paper, we prove that every Diophantine quadruple in Z[i][X] is regular. More precisely, we prove that if {; ; a, b, c, d}; ; is a set of four non-zero polynomials from Z[i][X], not all constant, such that the product of any two of its distinct elements increased by 1 is a square of a polynomial from Z[i][X], then (a + b - c - d)^2 = 4(ab + 1)(cd + 1).

Diophantine m-tuples ; Polynomials ; Regular quadruples

nije evidentirano