Theoretical Statistics and Mathematics Unit, ISI Delhi

March 28, 2012 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Shanta Laishram,
Indian Statistical Institute, Delhi

Title:
Squares and greatest prime factor in an arithmetic progression

Abstract of Talk

It is easy to see that there are infinitely many Arithmetic Progression(AP)s of length 2 and 3 which are all squares. Fermat proved that there are no four squares which are in AP. Euler generalised it by showing that a product of four consecutive terms of an AP can never be a perfect square. These have been extended in the works of Hirata-Kohno, Laishram, Shorey and Tijdeman and Bennett, Bruin, Gy\H{o}ry and Hajdu. It is an open problem to show that there is no AP of length at least four whose product of terms is a perfect square. In this talk, I will give an overview of this problem and some known results and also will talk about a new insight connecting greatest prime factor of product of terms of an AP with this problem.