engleski

On generalized problem of Diophantus in some number fields

The set of nonzero and distinct elements {;z1, z2, z3, z4}; in R such that zizj +w is a perfect square in R for 1 <= i < j <= 4 is called a Diophantine quadruple with the property D(w) in R, where R denotes a commutative ring with the unity. We consider the problem of existence of Diophantine quadruples with the property D(w) in rings of integers of some number fields.

Diophantine quadruples; number fields

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