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Math Help - Quick modular solutions question

  1. #1
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    Quick modular solutions question

    How do I solve:

    Find all soultions of x^2 \equiv -23 ( mod 240).

    Thanks!
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  2. #2
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    Quote Originally Posted by Proof_of_life View Post
    Find all soultions of x^2 \equiv -23 ( mod 240).
    240 is a multiple of 5, and -23\equiv2\!\!\!\pmod5. But the equation x^2\equiv2\!\!\!\pmod5 has no solutions. So it doesn't look as though x^2\equiv-23\!\!\!\pmod{240} has any solutions either.
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  3. #3
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    Yup, I figured it out. Thanks.
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