Let $p$ be a positive prime number different from $3$ and $a$ be an integer not divisible neither by $3$ nor by $p$. Show that in this case $a^{6p−6} \equiv 1 \pmod{9p}$
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3Not a bad time to share your effort after https://math.stackexchange.com/questions/3038266/determine-the-remainder-we-get-if-we-divide-799801-by-264 – lab bhattacharjee Dec 13 '18 at 17:10
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I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way. – Y.xin Dec 13 '18 at 17:16
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4Apply Euler's theorem, since $\varphi(9p)=\varphi(9)\cdot \varphi(p)$ – rtybase Dec 13 '18 at 17:17
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I don't know what's the next steps. I get φ(9p)= 6⋅φ(p). – Y.xin Dec 16 '18 at 18:09