Some super congruences involving binomial coefficients

Details Some super congruences involving binomial coefficients Some super congruences involving binomial coefficients

2010-06-15

arxiv.org/abs/1006.3069v1

Mathematics

Number Theory

9 pages

Scientific paper

Let $p>3$ be a prime. We show that $$T_{p-1}=(p/3)3^{p-1} (mod p^2},$$ where the central trinomial coefficient $T_n$ is the constant term in the expansion of $(1+x+x^{-1})^n$. We also prove three congruences conjectured by Sun one of which is as follows: $$\sum_{k=0}^{p-1}\binom{p-1}{k}\binom{2k}{k}((-1)^k-(-3)^{-k})=(p/3)(3^{p-1}-1) (mod p^3).$$

Affiliated with

Also associated with

No associations

Rating

Some super congruences involving binomial coefficients 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 Some super congruences involving binomial coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some super congruences involving binomial coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-105734