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Math Help - squared series...

  1. #1
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    squared series...

    I was dealing with a problem in a book by David M. Burton.The question is :
    Prove that no integer in the following sequence is a perfect square:
    11,111,1111,11111,......


    thanks

    kaka
    Last edited by kaka1988; April 25th 2010 at 01:44 AM. Reason: Thw quote tags are not used in starting a thread...
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  2. #2
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    Quote Originally Posted by kaka1988 View Post
    I was dealing with a problem in a book by David M. Burton.The question is :
    Prove that no integer in the following sequence is a perfect square:
    11,111,1111,11111,......


    thanks

    kaka

    Every integer squared equals 0\,\,\,or\,\,\,1\!\!\!\pmod 4 . As none of 11,111,1111,\ldots is even, this means that if any of these numbers is a square then (111\ldots 1)-1=0\!\!\!\pmod 4 . Check that this is impossible.

    Tonio
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