How many number of ordered pairs $(a, b)$ where $a,b, \in \{1, 2,\ldots,100\}$ such that $7^a + 7^b$ is divisible by 5?
I am not sure how to do this. Any ideas?
EDIT:
I noticed that if $a$ is of the form $4k+1$ then $b$ is of the form 4k'+3 (where k,k' \in \{ 0 \} $\cup \space\mathbb{N}$).
Similarly, another possible pair would be (4k,4k'+2),now we have to count the number of ordered pair of the form (4k,4k'+2),$(4k+1,4k'+3)$,$(4k'+2,4k)$,$(4k'+3,4k+1)$ in $\{1, 2,\cdots,100\}$. However,I haven't figured out (yet) how to do this?