engleski

A Diophantine problem in Z[(1+√ d)/2]

We characterize the existence of infinitely many Diophantine quadruples with the property D(z) in the ring Z[(1+sqrt(d))/2], where d is a positive integer such that the Pellian equation x^2 − dy^2 = 4 is solvable, in the terms of the representability of z as a difference of two squares.

Quadratic fields; Diophnatine quadruples

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