<s>[INST] Prove for any integer $a$, one of the integers $a$, $a+2$, $a+4$ is divisible by $3$. Prove for any integer $a$, one of the integers $a$, $a+2$, $a+4$ is divisible by $3$. 
I know I would use the division algorithm but I am really confused how to go about this. Step by step explanation please? thank you so much!
 [/INST] For every number $a$: $a \equiv {0, 1, 2} \pmod{3}$
In the first case: $a \equiv 0 \pmod{3}$
For the second one:
$a \equiv 1 \pmod{3}$ =>
$a+2 \equiv 3 \pmod{3} \equiv 0 \pmod{3}$
For the third one:
$a \equiv 2 \pmod{3}$ =>
$a+4 \equiv 6 \pmod{3} \equiv 0 \pmod{3}$
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