Hey /sci/, I stumbled upon something in the field of Mathematics.

It took me a while but I've finally expressed what I've stumbled upon in Mathematical language. Any natural number that can be expressed as a power of another natural number can also be expressed as a sum of multiples of combinations (I'm temped to say "a linear combination of combinations" but perhaps that language is best reserved to linear algebra).

My question is, can this be developed and generalised even further?
Do you think it's possible to perhaps, express n^a in terms of combinations when a is a rational number? Would it help to perhaps redefine combinations using the Pi function instead so that perhaps then, it might be possible to have rational numbers in your combinations? If we're generalising, then I imagine we might need to use integration but I don't see how one might end up taking lots of small sums in this scenario.

If anyone sees any potential in this, please tell me, even if you end up using Mathematical language that I don't understand. I do intend to study Maths properly so I believe that I, in time, will come to understand what you said.