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I got an assigment for homework and haven't got a clue about how to solve it, it goes as follows:

"Given a set of 12 integers, demonsrate that the subtraction of 2 integers of said set is divisible by 11"

Any help? Thank you.

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1 Answer 1

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What this seems to mean is that in any set of twelve integers, there is at least one pair whose difference is divisible by 11.

Hint: use the pigeonhole principle when looking at the remainders when each of your twelve integers are divided by 11.

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I do understand the pigeonhole principle, but I'm not sure about applying it to infinite sets, could you please be more specific? Thanks! –  Darkkurama Nov 30 '11 at 10:03
    
@Darkkurama: Try to choose 12 integers and look at their remainders when dividing by 11. See if any match. Then try another 12 integers. Then think about the pigeonhole principle again. –  Henry Nov 30 '11 at 10:05
    
@Darkkurama: The set of integers we are looking at has 12 elements. What infinite set do you mean? –  Zev Chonoles Nov 30 '11 at 10:06
    
Well the set is not infinite but its numbers can be any integer . –  Darkkurama Nov 30 '11 at 10:19

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