Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.5

Tags: number theory, divisible, divides



Let $a$ and $ b$ be even numbers, such that $M = (a + b)^2-ab$ is a multiple of $5$. Consider the following statements: I) The unit digits of $a^3$ and $b^3$ are different. II) $M$ is divisible by $100$. Please indicate which of the above statements are true with certainty.