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Math Help - Find all solutions of...

  1. #1
    Junior Member
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    Find all solutions of...

    i) Find (just by trial and error) all solutions of

    2x2 is congruent to 1 mod 17
    and
    2x2 is congruent to 1 mod 23
    ii) Now find all solutions of
    2x2 is congruent to 1 mod 391
    [Note: 391 = 17*23]
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  2. #2
    Member Haven's Avatar
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    Did you mean to write?

    2x^2 \equiv 1 \pmod{17} and 2x^2 \equiv 1\pmod{23}
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  3. #3
    Super Member Bacterius's Avatar
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    Note that if :

    x \equiv y \pmod{m}

    x \equiv y \pmod{n}

    Then :

    x \equiv y \pmod{mn}

    And your solution follows.

    This doesn't always work, I forgot how to do this, I need to check. I think it works anyway if both moduli are prime.
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  4. #4
    Junior Member
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    Quote Originally Posted by Haven View Post
    Did you mean to write?

    2x^2 \equiv 1 \pmod{17} and 2x^2 \equiv 1\pmod{23}
    Yeah. That's how it looked when I posted it, but the formatting was lost for some reason.
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