Question 12
Find all nonnegative integers $m$ and $n$ that satisfy the equation:
$$
107^{56}(m^2 - 1) - 2m + 3 = \binom{113^{114}}{n}.
$$
(If $n$ and $r$ are nonnegative integers satisfying $r \le n$, then $\binom{n}{r} = C_r^n = \frac{n!}{r!(n-r)!}$ and $\binom{n}{r} = 0$ if $r \gt n$.)
$$
107^{56}(m^2 - 1) - 2m + 3 = \binom{113^{114}}{n}.
$$
(If $n$ and $r$ are nonnegative integers satisfying $r \le n$, then $\binom{n}{r} = C_r^n = \frac{n!}{r!(n-r)!}$ and $\binom{n}{r} = 0$ if $r \gt n$.)