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Math Help - mods

  1. #1
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    mods

    623x is congruent to 4(mod 679)?
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  2. #2
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    Quote Originally Posted by meshel88 View Post
    623x is congruent to 4(mod 679)?

    This equation has no solution since 623x=4\!\!\!\pmod{679}\Longrightarrow 623x\cdot 4^{-1}=1\!\!\!\pmod{679} (why does 4^{-1}\!\!\!\pmod{679} exist?) \Longrightarrow 623 is a unit modulo 679 \Longleftrightarrow 623 is a unit

    in \mathbb{Z}_{679} , which is absurd as 623\,,\,\,679 are NOT coprime, as you can easily check.

    Tonio
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