How do I prove that the function defined as is an onto function by mathematical induction? The bracket meant "n choose r".

I started off this way:

Basis Step:

So f(1,1) is true since f(1,1)=1, the element "1" in the codomain has its preimages m=1 and n=1.

Then assume true for .

Inductive Step:

Then there exists a such that

So

But how do I continue to show that this will be true for all k+1 and that this is an onto function?

Are there any "easier tricks/process" when doing induction? I am trying to keep doing induction until I get the hang of it but I am always stuck after the basis step.

Doesn't feel like a friendly technique.

Thanks for any help.