I'm working on a computation which depends on the idea that given two natural numbers $x$ and $y$ where $y > x$, the product $x(y - x)$ will always be greater than $y$.
Is there a proof of this ? My elementary math is a bit rusty.
The simple evaluation gives : $xy - x^2$
I can't seem to formalize this relation with respect to $y$. Could somebody give me a refresher on the proof strategies for such a problem ?
*EDIT: * Apologies. I got lost in writing it here. It's actually $x (y - x + 1)$. So basically given two numbers this would result in the value above plus a summation series that is solvable using $x(x+1)/2$. Does that make more sense ? (P.S: thank you for the quick response.)