ALC Seminar | Speaker: Florian Luca (Stellenbosh University, South Africa)
Title: Carmichael numbers of special forms
Abstract: A Carmichael number is a composite positive integer N which behaves like a prime number with respect to Fermat’s Little theorem; that is a^N-a is a multiple of N for all integers a. It is known that there are infinitely many such numbers. In this talk, we will explore such numbers which have the form 2^n*k+1 for some odd integer k. The questions we can ask are. Fix k. What can we say about the numbers n such that 2^n*k+1 is Carmichael? Or, what can we say about the odd positive integers k such that N=2^n*k+1 is Carmichael number for some positive integer n? We will give some partial answers to these questions.