Residue Classes Having Tardy Totients

Details Residue Classes Having Tardy Totients Residue Classes Having Tardy Totients

2007-09-19

arxiv.org/abs/0709.3056v1

Mathematics

Number Theory

14 pages

Scientific paper

We show, in an effective way, that there exists a sequence of congruence classes $a_k\pmod {m_k}$ such that the minimal solution $n=n_k$ of the congruence $\phi(n)\equiv a_k\pmod {m_k}$ exists and satisfies $\log n_k/\log m_k\to\infty $ as $k\to\infty$. Here, $\phi(n)$ is the Euler function. This answers a question raised in \cite{FS}. We also show that every congruence class containing an even integer contains infinitely many values of the Carmichael function $\lambda(n)$ and the least such $n$ satisfies $n\ll m^{13}$.

Affiliated with

Also associated with

No associations

Rating

Residue Classes Having Tardy Totients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Residue Classes Having Tardy Totients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Residue Classes Having Tardy Totients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-337062