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## Homework Statement

Prove that 3 divides one of the integers n, n + 2, or n + 4, for any integer n.

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- Thread starter dgentile
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Prove that 3 divides one of the integers n, n + 2, or n + 4, for any integer n.

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Dick

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Try, ok? Any integer n has a remainder of either 0, 1 or 2 when divided by 3. Come on.

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Okay...so whats the formula for proving that true is my question?

Thanks

Thanks

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Dick

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[tex] n=3q+r,[/tex]

[tex]n+2=3q_1+r[/tex]

[tex]n+4=3q_2+r[/tex] [tex]0\leq r<3[/tex]

i.e r=0, 1 or 2

Now, say if r=0, what happens? if r=1, what happens? if r=2 what happens?

P.S. This is what Dick said, i just wanted to make a little bit easier on you.

YOu MUST show your work next time.

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