Problem

Source: Gulf Mathematical Olympiad GMO 2017 p4

Tags: ceiling function, power of 2, divides, maximum, number theory



1 - Prove that $55 < (1+\sqrt{3})^4 < 56$ . 2 - Find the largest power of $2$ that divides $\lceil(1+\sqrt{3})^{2n}\rceil$ for the positive integer $n$