Prove that the congruence (x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p) has a solution for every prime p. No idea how to do this, can anyone help?
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Originally Posted by johndoe3344 Prove that the congruence (x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p) has a solution for every prime p. No idea how to do this, can anyone help? If $\displaystyle \left(\frac2p\right)=1 $ or $\displaystyle \left(\frac{17}{p}\right)=1 $ then we're done. Otherwise $\displaystyle \left(\frac{34}{p}\right)=\left(\frac2p\right)\lef t(\frac{17}{p}\right) = (-1)(-1) = 1 $
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