Type: Article

Least totients in arithmetic progressions

Javier Cilleruelo; Moubariz Z. Garaev;

Abstract:

Let N(a, m) be the least integer n (if it exists) such that phi(n) equivalent to a (mod m). Friedlander and Shparlinski proved that for any epsilon > 0 there exists A = A(epsilon) > 0 such that for any positive integer m which has no prime divisors p < (logm)(A) and any integer a with gcd(a,m) = 1, we have the bound N(a, m) << m(3+epsilon). In the present paper we improve this bound to N(a, m) << m(2+epsilon).