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Math Help - Possible remainders

  1. #1
    Senior Member OReilly's Avatar
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    Possible remainders

    What are possible remainders when dividing with 9 squares of natural numbers?
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  2. #2
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    Quote Originally Posted by OReilly
    What are possible remainders when dividing with 9 squares of natural numbers?
    You can attack the problem with Division Algorithm.

    Meaning any number must be exactly in one of these forms,
    9k
    9k+1
    9k+2
    .........................
    9k+8

    When you square then, you get, the only possibilities,
    9k
    9k+1
    9k+4
    9k+7
    Thus, remainders are 0,1,4,7
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  3. #3
    Senior Member OReilly's Avatar
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    I must say I didn't think of that!
    This problem has destroyed me! Whole day I couldn't solve it. Problems with divisibility are giving me most hard times and usually I can't solve them!
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