Every Number Serves A Purpose

Number Theory Level 1

15 is not divisible by 6.
But for an integer $A$ , the product $15\times A$ is divisible by 6.

Is it true that $A$ must be divisible by 6?

Yes, it is true No, it is not true

2 solutions

Ronald Chén
Nov 6, 2016

No. For example, A might be 2. The reason is that the number 3, which is one of the prime factors of the number 6, also belongs to the decomposition of the number 15. Thus we can only be sure that A is even.

Maybe this problem should be extended by replacing 15 and 6 with variables so that you cannot find the number 2.

William Nathanael Supriadi - 4 years, 7 months ago

Viki Zeta
Nov 7, 2016

$6|15A \\ \implies 15A = 6m + 0 \\ \implies 5A = 2m \\ \implies 2 | 5A \\ \implies 2 | A$

$15A \equiv 0 ~ \mathrm{mod}~6 \\ \implies 5A \equiv 0 ~ \mathrm{mod}~2\\ \implies A \equiv 0 ~ \mathrm{mod} 2$

Every Number Serves A Purpose

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