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Thread: computing quadratic congruence

  1. #1
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    computing quadratic congruence

    Find all the incongruent solutions of the following quadratic congruence.

    X^2 is congruent to 53 mod 143
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    Quote Originally Posted by JCIR View Post
    X^2 is congruent to 53 mod 143
    This is equivalent to,
    $\displaystyle x^2\equiv 54 (\bmod 11)$ and $\displaystyle x^2\equiv 54(\bmod 13)$
    Which reduces to,
    $\displaystyle x^2 \equiv 10 (\bmod 11)$ and $\displaystyle x^2 \equiv 2(\bmod 13)$
    This has no solutions.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    This is equivalent to,
    $\displaystyle x^2\equiv 54 (\bmod 11)$ and $\displaystyle x^2\equiv 54(\bmod 13)$
    Which reduces to,
    $\displaystyle x^2 \equiv 10 (\bmod 11)$ and $\displaystyle x^2 \equiv 2(\bmod 13)$
    This has no solutions.
    The question asked for 53, not 54.

    And this question is the same as occurred in this thread.
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