Mathematics – Number Theory
Scientific paper
2005-08-04
Trans. Amer. Math. Soc. 359(2007), no.11, 5525-5553
Mathematics
Number Theory
Scientific paper
Let p be any prime, and let a and n be nonnegative integers. Let $r\in Z$ and $f(x)\in Z[x]$. We establish the congruence $$p^{\deg f}\sum_{k=r(mod p^a)}\binom{n}{k}(-1)^k f((k-r)/p^a) =0 (mod p^{\sum_{i=a}^{\infty}[n/p^i]})$$ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If a is greater than one, and $l,s,t$ are nonnegative integers with $s,t
Davis Donald M.
Sun Zhi-Wei
No associations
LandOfFree
Combinatorial congruences modulo prime powers 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 Combinatorial congruences modulo prime powers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorial congruences modulo prime powers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-614777