IMAS 2018–2019 Junior — Round 2 Question 1

Question 1

1. If $a$ divides $b$ and $k$ is an integer, then $a$ divides $kb$.
2. If $a$ divides $b$ and $b$ divides $c$, then $a$ divides $c$.
3. If $a=bc$, and $b,c$ are positive integers, then $a$ is divisible by $b$ or $c$.
4. If $b$ divides $a$ and $c$ divides $a$, then $bc$ divides $a$.
5. If $p\mid bc$, then $p\mid b$ or $p\mid c$, where $p$ is a prime number, $b$ and $c$ are integers.