# Math Help - More mod

1. ## 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).

2. Originally Posted by CoraGB
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

3. 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

4. notice that x^9 = sqrt(x^18) = +1 or -1 ......