An elementary proof of a congruence by Skula and Granville

Details An elementary proof of a congruence by Skula and Granville An elementary proof of a congruence by Skula and Granville

2011-08-11

arxiv.org/abs/1108.2361v1

Mathematics

Number Theory

pages 7

Scientific paper

Let $p\ge 5$ be a prime, and let $q_p(2):=(2^{p-1}-1)/p$ be the Fermat
quotient of $p$ to base 2. The following curious congruence was conjectured by
L. Skula and proved by A. Granville $$ q_p(2)^2\equiv
-\sum_{k=1}^{p-1}\frac{2^k}{k^2}\pmod{p}. $$ In this note we establish the
above congruence by entirely elementary number theory arguments.

Affiliated with

Also associated with

No associations

Rating

An elementary proof of a congruence by Skula and Granville 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 An elementary proof of a congruence by Skula and Granville, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An elementary proof of a congruence by Skula and Granville will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-275811