Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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

Given any seventeen integers, show that there is at least one subset of nine integers whose sum is divisible by $9$.

(one of my friend suggest me) may be this theorem helpful

Theorem: Given any $2n-1$ integers, there is at least one subset of $n$ integers whose sum is divisible by $n$.

and also Fermat’s Little Theorem can be used

share|cite|improve this question
I have known some problems of this category handled well with the pigeon hole principle. Have you given it a try? – Aseem Dua Nov 24 '12 at 5:53
@ Aseem Dua may be.... – UnknownController Nov 24 '12 at 6:10
up vote 3 down vote accepted

Here is a generalization of the problem to which you are referring, namely the fact that given any $2n-1$ integers there exists a subset of $n$ integers divisible by $n$. Applying the theorem to the case of $n=9$ provides the desired result.

share|cite|improve this answer
thank you....... – UnknownController Nov 24 '12 at 6:20

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.