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Math Help - Sum of digits of squares

  1. #1
    Like a stone-audioslave ADARSH's Avatar
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    Sum of digits of squares

    Hello all,
    Q. How many numbers between 1-2000 , have sum of digits of respective squares as 21 ?
    I am interested to know the working rather than the answer, Thanks to all
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ADARSH View Post
    Q. How many numbers between 1-2000 , have sum of digits of respective squares as 21 ?
    The sum of the digits of a number is congruent to the number itself mod 9. So the sum of the digits of n^2 is congruent to n^2 mod 9. But a square has to be congruent to 0, 1, 4 or 7 (mod 9), and 21 is congruent to 3 (mod 9).

    Conclusion: There are no numbers satisfying that condition.
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