Let $ A$ be a set of natural numbers in which if $ a$ , $ b$ belong to $ A$ ($ a>b$) then either $ a+b$ or $ a-b$ belong to $ A$ ( both cases may be posible at the same time). Decide wheter there is or not a set $ A$ consisting on exactly $ 100$ elements which has four elements $ x$, $ y$ , $ z$ , $ w$ ( not necesarilly distinct) that satisfy $ x-y=512$ and $ z-w=460$ Daniel