A positive integer is a Zumkeller number if its positive divisors can be partitioned into two disjoint sets with the same sum. For example, $6$ is a Zumkeller number because we can partition the positive divisors of $6$ into two disjoint sets $\{1, 2, 3\}$ and $\{6\}$, and the sum of elements of the two sets are equal. Santa defines a ridiculous number $R_n$ to be a number of the form $$R_n = m^2 - 69m - (n^2 - 69n)$$such that $R_n$ is also a Zumkeller number ($m$ and $n$ are positive integers). Santa is lazy this year, so he decides to fix $n \in N$ and give as many gifts as there are ridiculous numbers $R_n$. Prove that Santa’s plan is flawed as for any $n \in N$, there are infinitely many ridiculous numbers $R_n$.