I like to calculate $n$ for the the division $2^n/(n(n+1))$ with the remainder result $2$. This is easy for small $n$, but if I use large $n$, the power of $2$ result is growing very rapid. So it may be that with an intelligent mod calculation to simplfy the formular, especially to avoid the high power of $2$ results or to reduce the exponent with an intelligent mod simplification.
Thanks for helping :)