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Topic: application of pigeonhole principle
Replies: 2   Last Post: Nov 17, 2011 8:58 PM

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Posts: 2
Registered: 11/17/11
application of pigeonhole principle
Posted: Nov 17, 2011 12:19 AM
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Hello, i am asking for help of using pigeonhole principle.

It is given 13 integers c_1,c_2,...c_13(some of them may be the same). Use pigeonhole principle to prove that there exist i and j with 0<=i<j<=13 such that
c_i+c_(i+1)+c_(i+2) =...=c_j is divisible by 13, for example c_4+c_5+c_6+c_7 is divisible by 13.
(Hint: consider the following 13 integers n_1=c_1, n_2=c_1+c_2,...n_13=c_1+c_2+...+c_13 and their remainder when divided by 13)

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