1. Least totients in arithmetic progressions.
- Author
-
Javier Cilleruelo and Moubariz Z. Garaev
- Subjects
- *
MATHEMATICAL proofs , *NUMERICAL analysis , *MATHEMATICS , *ARITHMETIC series , *INTEGERS - Abstract
Let $N(a,m)$ be the least integer $n$ (if it exists) such that $varphi (n)equiv apmod m$. Friedlander and Shparlinski proved that for any $varepsilon >0$ there exists $A=A(varepsilon )>0$ such that for any positive integer $m$ which has no prime divisors $p<(log m)^A$ and any integer $a$ with $gcd (a,m)=1,$ we have the bound $N(a,m)ll m^{3+varepsilon }.$ In the present paper we improve this bound to $N(a,m)ll m^{2+varepsilon }.$ [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF