Theory of Relative Squares

[Thor23]

Yeah, I was just going off my notes from my Discrete Math class, and what you wrote didn't look like any of my notes, so it didn't seem right to me. I am pretty sure, though, that induction is the sort of thing you would use to prove something like this, so I don't think there's any problem there.

Fun Fact: If you include the previous term (S(k-1)) in there, then you have recurrence relation that will tell you what the square of the number after it is. I.E. putting in 20 will get you 21^2.