I'm stuck with this problem from my algebra class. We've recently been introduced to Fermat's little theorem and the Chinese Remainder Theorem.
Let $a \in \Bbb Z$ such that $gcd(9a^{25}+10:280)=35$. Find the remainder of $a$ when divided by 70.
So far I've tried to solve the congruence equation $9a^{25} \equiv -10 \pmod {35}$. The result for (using inverses and Fermat's theorem) is $a \equiv 30 \pmod {35}$
If this is ok, what should I do next? Thanks!