Question 116
Let $m, n$ be positive integers such that $\gcd(m, n)=1$, where $a \wedge b$ denotes the greatest common divisor of $a$ and $b$. What value(s) can
$$
\left(2^{m}-2^{n}\right) \wedge \left(2^{m^{2}+m n+n^{2}}-1\right)
$$
take?
$$
\left(2^{m}-2^{n}\right) \wedge \left(2^{m^{2}+m n+n^{2}}-1\right)
$$
take?