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## 09S Primitive Roots: Revisited

09. PEN B6 Suppose that $m$ does not have a primitive root. Show that

$a{}^{{}^\frac{\varphi(m)}{2}} \equiv 1 \; (mod \; m)$

for every $a$ relatively prime to $m$.

Here is the official solution file: pen09.
You can also disscuss the problems here!

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