1. 2. 3. Let a, b E Z. Prove that if a 2 5, then af b or ai' (b+ 3). Prove that V5 is irrational. Prove that % 2.1x/24 is irrational. Let S = {mx/E+ n | m, n E Z}. Prove that for every x E S the pair of integers m. n E Z such that x = m\\/+ n is unique