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Math Help - need help

  1. #1
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    need help

    prove that any number that is a square must have one of the following for its units digit: 0,1,4,5,6,9.
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  2. #2
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    Quote Originally Posted by mancillaj3 View Post
    prove that any number that is a square must have one of the following for its units digit: 0,1,4,5,6,9.
    The squares modulo 10 are: 0,1,4,5,6,9.
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  3. #3
    Member arpitagarwal82's Avatar
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    Consider a two digit number with unit digit as a and tens digit as b
    So a and b both are positive interger less than 10
    So number can be written as 10b + a

    Now (10b + a)^2 = 100b^2 + 20ab + a^2

    Now 100b^2 and 20ab both have 0 at unit place. So unit digit of 100b^2 + 20ab + a^2 will be decided by a^2

    And for a being single digit integer, you only get 0,1,4,5,6,9.at units place of a^2.

    You can extend this proof for three digit number 100c + 10b + a.
    Same logic will be applied in this case
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