Application of Fermat's Little Theorem/Fermat Euler Theorem Find an integer $x$ with $0\leq x \leq73$ such that $$2^{75}\equiv x \pmod{74}$$
I think I'm supposed to be using either Fermat's Little Theorem or the Fermat-Euler theorem here but I don't think I can do it directly because $74$ is not prime nor do I have $\operatorname{hcf}(2,74)=1.$
What should I be doing?

$$2^{75}\equiv x \pmod{74} \Rightarrow \frac{2^{75}}{2} \equiv \frac{x}{2} \left(\text{mod}{\frac{74}{2}}\right) \Rightarrow 2^{2 \cdot 37} \equiv \frac{x}{2} \pmod{37} \\ 
4^{37} \equiv \frac{x}{2} \pmod{37}$$
$37$ is prime, so you can apply Fermat Little Theorem. That is:
$$a^{37} \equiv a \pmod{37} \Rightarrow \frac{x}{2} = 4 \Rightarrow x = 8.$$
