<s>[INST] Inverse | Modulo | Power Describe the inverse of $5$ modulo $18$ as a positive power of $5\pmod{18}$.

I've got that the inverse of $5$ is $11$, but is this question asking to find a $t$ such that
$$ 11=5^t\pmod{18}?$$
 [/INST] $$5^2=25\equiv 7\equiv-11 \pmod {18}, \quad 5^3\equiv 5\cdot7\equiv-1 \pmod {18}$$
$$\implies 11=(-11)(-1)\equiv 5^2\cdot5^3\equiv5^5 \pmod {18}$$
Now, as $5^3\equiv-1 \pmod {18}, 5^6=(5^3)^2\equiv(-1)^2\equiv1$
$\implies 5^{6u}=(5^6)^u\equiv1^u\equiv1\pmod{18}$ for any integer $u$
So, the general solution will be $t=6u+5$ as $5^{5+6u}\equiv1\cdot5^5\equiv1\cdot11 \pmod {18}$
If we need $5+6u>0, u\ge 0$ 
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