Type: Article

A note on the least totient of a residue class

M. Z. Garaev;

Abstract:

Let q be a large prime number, a be any integer and epsilon be a fixed small positive quantity. Friedlander and Shparlinksi (Least totient in a residue class, Bull. London Math. Soc. 39 (2007), 425-432) have shown that there exists a positive integer n < q(5/2+epsilon) such that phi(n) falls into the residue class a (mod q. Here, phi(n) denotes Euler's function. In the present paper we improve this bound to n < q(2 + epsilon).