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4 March, 02:22

Prove that among 502 positive integers, there are always two integers so that either their sum or their difference is divisible by 1000.

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  1. 4 March, 02:51
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    We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.

    Step-by-step explanation:

    We have a 502 positive integers. Therefore we have a numbers 1, 2, 3, ..., 500, 501, 502.

    For the sum, we can choose the numbers 502 and 488. We get

    (502+488) / 1000=1000/1000=1.

    For the difference, we can choose the numbers 1 and 501. We get

    (1-501) / 1000=-500/1000=-0.5.

    We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.
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