Question

Prove that one and only one out of n, n+2 and n+4 is divided by 3, where n is any
positive integer.

Answer 1

Answer:

nice

Step-by-step explanation:

Answer 2

Answer : True

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First, when $n=3k$.

This is unnecessary.

To Prove : Let $n=3k$(A Multiple Of 3).

Then, $n+2=3k+2$.

Also, $n+4=3(k+1)+1$.

∴ $n$ is a multiple of 3.

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Second, when $n=3k+1$.

To Prove : Let $n=3k+1$.

Then, $n+2=3(k+1)$.

Also, $n+4=3(k+1)+2$.

∴ $n+2$ is a multiple of 3.

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Last, when $n=3k+2$.

To Prove : Let $n=3k+2$.

Then, $n+2=3(k+1)+1$.

Also, $n+4=3(k+2)$.

∴ $n+4$ is a multiple of 3.

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Hence proved.

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