Find all integers $a, b, c$ such that $2^{a}+9^{b}=2 \cdot 5^{c}-7$
When looking modulo 4, we get a contradiction if $a \geq 2$. If $a=1$, then by looking modulo 3 we get $b=0$, and $(a, b, c)=(1,0,1)$. If $a=0$, by considering the parity we show that there are no solutions.