turkmath.org

An integer n is called squarefull (or powerful) if in its prime factorization all the prime factors have exponents greater than 1. In this talk, we connect several seemingly unrelated conjectures of Ankeny, Artin, Chowla and Mordell to a conjecture of Erdos on consecutive squarefull numbers. We then study the 'Erdos conjecture' and relate it to the 'abc conjecture'. We also derive by elementary methods several unconditional results pertaining to the Erdos conjecture. This is a joint work with Prof. M. Ram Murty.