Proving 3 Divides at Least One Integer

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To prove that 3 divides one of the integers n, n + 2, or n + 4 for any integer n, consider the possible remainders when n is divided by 3, which are 0, 1, or 2. If n has a remainder of 0, then n is divisible by 3. If n has a remainder of 1, then n + 2 will be divisible by 3. If n has a remainder of 2, then n + 4 will be divisible by 3. The proof relies on examining each case of the remainder, confirming that at least one of the three integers is divisible by 3. This demonstrates the validity of the statement for any integer n.
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Homework Statement



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


Homework Equations





The Attempt at a Solution


 
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Try, ok? Any integer n has a remainder of either 0, 1 or 2 when divided by 3. Come on.
 
Okay...so what's the formula for proving that true is my question?

Thanks
 
Read the forum rules. You are supposed to put something in the "attempt at a solution section". I just gave you a hint. There really is no 'formula'.
 
Let n be any such integer. THen by the division algorithm there exist integers q and r such that

n=3q+r,

n+2=3q_1+r

n+4=3q_2+r 0\leq r<3

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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