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# Prove or disaprove that if a|bc, where a, b, and c are positive integers and a≠0a, then a|b or a|c.

Discrete math
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asked 2021-02-01

Prove or disaprove that if a|bc, where a, b, and c are positive integers and $$\displaystyle{a}≠{0}{a}$$, then $$a|b$$ or $$a|c$$.

## Expert Answers (1)

2021-02-02

False! Take $$b=c=2$$ and $$a=4.$$

Then clearly a does not divide b nor c, but a divides bc.

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