Obvious Part [quote] X*X=A X+Y=B Y*Y=C Y=X+1 [/quote] Interesting Part [quote] A+B=C [/quote] X*X+X+Y=C X*X+X+X+1=C (X^2)+2X+1=C (Where C is the square of the of X+1) (X^2)+2X+1=(X+1)(X+1) It's a parabolic function with a root at negative one, but other than that I can't find anything really substantive about it. I vaguely recall using a property similar to this for an iterating loop in Matlab once, but if that's what this is then it's one of the many things Euler pointed out. I'm not familiar enough with whatever theory is applicable to this to say anything more about the possible significance. It could possibly be useful though if you needed to tell a code to find the square above a given value and you didn't want to just put (n+1)^2 for some reason (maybe n is defined symbolically and ^2 would take more computation time than your method in a given scenario). Kind of neat though.