A number \(n\) is an integer such that \(n\) is not divisible by \(3\) or by \(2\). Show that \(n^2-1\) is divisible by \(24\).
Show that for any two positive real numbers \(x,y\) it is true that \(x^2+y^2 \ge 2xy\).
Find all pairs of integers \((x,y)\) so that the following equation is true \(xy = y+x\).