Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can I prove the following, where $p$ is a prime and $x$ a positive integer?


I'm not sure if it is actually true, but I tested for small numbers and it checked.

share|improve this question
Are you aware that the expressions you've written are binomial coefficients? –  Zev Chonoles Jul 29 '12 at 15:38
Also, see this question for the case of $p=2$. –  Zev Chonoles Jul 29 '12 at 15:40
This is a special case of Babbage's theorem (en.wikipedia.org/wiki/…). –  Micah Jul 29 '12 at 15:52
It seems to be true also for $\mod p^3$ at least when $p>3$, all primes up to 101. –  i. m. soloveichik Jul 29 '12 at 15:54
I was not aware of Babbage's theorem, it does solve it indeed. Here's an algebraic proof of the theorem: answers.yahoo.com/question/index?qid=20100810104024AAhqaaJ –  Ricbit Jul 29 '12 at 16:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.