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Math Help - More mod

  1. #1
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    More mod

    I am looking for some help using Wilson's Theorem for the following problem 29!(mod 31).

    And then I am quite stumped with proving that the following has no solutions: x^18 + x^9 + 1 = 0 (mod 19).
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  2. #2
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    Quote Originally Posted by CoraGB View Post
    I am looking for some help using Wilson's Theorem for the following problem 29!(mod 31).

    And then I am quite stumped with proving that the following has no solutions: x^18 + x^9 + 1 = 0 (mod 19).

    29!=\frac{30!}{30}=\frac{-1}{-1}\!\!\!\!\pmod{31} ....

    For two use again Wilson's theorem...you may want to check x=0\,\,\,and\,\,\,x\ne 0 separatedly.

    Tonio
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  3. #3
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    Thank you for your help. I am still kind of struggling with #2. I simplified the x^18 to 1 mod 19, so I have x^9 +2 = 0(mod 19). Does that work, if so where should I go for there?
    Thank you again
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  4. #4
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    notice that x^9 = sqrt(x^18) = +1 or -1 ......
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