Number Theory

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If $a | b$ and $a | c$, then ...

NUMTH-VJRJ0J

Let $a, b, c \in \mathbb{Z}$. If $a | b$ and $a | c$, then which of the following conclusions are true?

Select ALL that apply.

A

$a | bc$

B

$a | bx + cy$, where $x, y \in \mathbb{Z}$

C

$a^2 | b$ and $a^2 | c$

D

$a^2 | bx + cy$, where $x, y \in \mathbb{Z}$