<s>[INST] Quick way to solve $16x \equiv -9 \pmod {3^5}$ Quick way to solve $16x \equiv -9=234 \pmod {3^5}$
Any hints?
I tried all the numbers from $1$ to $10$ but none work.
 [/INST] Hint:
If $16x \equiv -9 \bmod {3^5}$, then $16x \equiv -9 \bmod {3^2}$ and so $x \equiv 0 \bmod {3^2}$.
Let $x=9y$. Then we can cancel $9$ in $16x \equiv -9 \bmod {3^5}$ and get $16y \equiv -1 \bmod {3^3}$, which is simpler.
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