Problem - 123
Find all positive integer $n$ such that $2^n+1$ is divisible by 3.
Because
$$2^n+1\equiv (-1)^n + 1\equiv 0\pmod{3}$$therefore, all qualifying $n$ are odd.
Because
$$2^n+1\equiv (-1)^n + 1\equiv 0\pmod{3}$$therefore, all qualifying $n$ are odd.