I'm having a huge problem even understanding what to do here. Any guidance to get me going would be greatly appreciated.
If $n,k$ are positive integers, how many integral solutions are there to the equation $$ x_1+x_2+ \cdots +x_k=n $$ if for all $i$, $x_i\geq2i$.
I've tried creating the equations for n=1 and on up, but that's not providing me any answers or patterns. Any help would be greatly appreciated. I think I need to create a weight function somehow, but even then I'm lost. Thank you.