MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Any hints how to compute this sum $$\sum_{i=1}^{N-1}\left[i\frac{K}{N}\right]^{p}?$$ where K < N , $\left[\cdot\right]$ denotes fractional part, $p\in N$

share|cite|improve this question
May I suggest that you not use $[x]$ for fractional part when everyone else uses it for integer part? Standard is $\lbrace x\rbrace$. – Gerry Myerson Jul 9 '10 at 23:24
I think the best hint is that the sum is independent of K when gcd(K,N) = 1. – François G. Dorais Jul 10 '10 at 1:23
up vote 3 down vote accepted

The article On Certain Sums of Fractional Parts by Gandhi and Williams answers your question for $p=1$; it's likely that since 1974 this result has been generalized, but I wasn't able to find a reference.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.