engleski

There does not exist a D(4)-sextuple

A set of m positive integers is called a D(4)-m-tuple, if the product of any two of its distinct elements increased by 4 is a perfect square. There is a conjecture that D(4)-triple {; ; ; a, b, c}; ; ; can be extended to a D(4)-quadruple{; ; ; a, b, c, d}; ; ; such that d > max{; ; ; a, b, c}; ; ; in the unique way. That was proved for D(4)-triple {; ; ; 1, 5, 12}; ; ; and various parametric families of D(4)-triples. We prove that there does not exist a D(4)-sextuple.

Pellian equations

nije evidentirano