Скачать или смотреть The generalised Diophantine m-tuples

Speaker: Anup Dixit, Institute of Mathematical Sciences

Fields Number Theory Seminar
http://www.fields.utoronto.ca/activit...

Abstract: A set of natural numbers {a1,a2,⋯,am} is said to be a Diophantine m-tuple with property D(n) if aiaj+n is a perfect square for i≠j. One may ask, what is the largest m for which such a tuple exists. This problem has a long history, attracting the attention of many, including Fermat, Baker, Davenport etc, with significant progress made in recent times due to Dujella and others. In this talk, we consider a similar question by replacing the condition aiaj+n from being a square to k-th powers. This is joint work with Ram Murty and Seoyoung Kim.