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Math Help - Counterexample

  1. #1
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    Counterexample

    Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers.
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  2. #2
    A Plied Mathematician
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    I would look fairly low. Just start at zero and work your way up.
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  3. #3
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    I am not sure how to go about this.
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  4. #4
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    Quote Originally Posted by lm6485 View Post
    I am not sure how to go about this.
    Follow Ackbeet's advice; try to write 1 as the sum of three squares; then try to write 2 as the sum of three squares; ... and if you get stuck say where you got stuck. The smallest positive integer not expressible as the sum of three squares is less than 10.
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