engleski

There are only finitely many D(4)-quintuples

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. The author have proven that there does not exist a D(4)-sextuple. In this talk we improve that result by showing that there are only finitely many D(4)-quintuples.

Diophantine m-tuples

nije evidentirano