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- W2964256043 abstract "In this paper we prove that every Diophantine quadruple in R[X] is regular. In other words, we prove that if {;a, b, c, d}; is a set of four non-zero elements of R[X], not all constant, such that the product of any two of its distinct elements increased by 1 is a square of an element of R[X], then (a+b−c−d)^2=4(ab+1)(cd+1). Some consequences of the above result are that for an arbitrary n ∈N there does not exist a set of five non-zero elements from Z[X], which are not all constant, such that the product of any two of its distinct elements increased by n is a square of an element of Z[X]. Furthermore, there can exist such a set of four non-zero elements of Z[X] if and only if n is a square." @default.
- W2964256043 created "2019-07-30" @default.
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- W2964256043 date "2017-09-19" @default.
- W2964256043 modified "2023-09-27" @default.
- W2964256043 title "A polynomial variant of a problem of Diophantus and its consequences" @default.
- W2964256043 hasPublicationYear "2017" @default.
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