Number Theory: How to solve $^{95} ≡ 2\; (mod\; 119)$?

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$^{95} ≡ 2\; (mod\; 119)$

I know that $119 = 17.7$ and therefore

$^{95} ≡ 2\; (mod\; 7)$ and $^{95} ≡ 2\; (mod\; 17)$.

By Euler Theorem, we have that $x^{\phi(m)} ≡ 1\; (mod\: m)$, when $gcd(x,m) = 1$.

Since $\phi(119) = \phi(17).\phi(7) =16.6 = 96$, we have that

$x^{96} ≡ 1 \; (mod\;119).$

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You have that $x^{96} \equiv 1 \pmod {119}$. So since $x^{95} \equiv 2$ we obtain $1 \equiv x^{96} \equiv 2x$, which yields $x = 60$.