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Math Help - Stuck on a congruency problem

  1. #1
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    Stuck on a congruency problem

    I'm using Wilson's Theorem to find the remainder of 24! when divided by 29. Here are my steps thus far:

    24!*25*26*27*28 ≡ -1 mod 29

    24!*(-4)*(-3)*(-2)*(-1) ≡ -1 mod 29

    24!*24 ≡ -1 mod 29

    How do I finish off the congruency to find the remainder?
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  2. #2
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    Quote Originally Posted by F350 View Post
    I'm using Wilson's Theorem to find the remainder of 24! when divided by 29. Here are my steps thus far:

    24!*25*26*27*28 ≡ -1 mod 29

    24!*(-4)*(-3)*(-2)*(-1) ≡ -1 mod 29

    24!*24 ≡ -1 mod 29

    How do I finish off the congruency to find the remainder?
    That's a good start. In fact, you're nearly there. Next step is to say that 24 ≡ 5 (mod 29), so 24!*5 ≡ 1 (mod 29). Finally 5*6 = 30 ≡ 1 (mod 29), so multiply both sides by 6 and you finish with 24! ≡ 6 (mod 29).
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