Assume $a+b+c=5^{1402}$. Find All integer values for $a$, $b$ and $c$ where $a$, $b$ and $c$ have the same amount of digits.
I honestly tried to multiply both sides by $2^{1402}$, which I think is pretty irrelevant. I have no Idea how to solve something like this. I would be happy if anyone could help.