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## Answers

Case 1 when n = 3q

n = 3q

, this is divisible by 3

n +2 = 3q + 2,

this is not divisible by 3

n + 4 = 3q + 4, this is also not divisible by 3

Case 2

when n = 3q + 2

n = 3q + 2, this is not divisible by 3

n + 2 = 3q +2+2=3q+4, this is not divisible by 3

n+4 = 3q+2+4 = 3q +6 = 3(q+2), this is divisible by 3

Case 3

when n = 3q + 1

n= 3q + 1, not divisible

n+2 = 3q+1 + 2= 3q + 3 = 3(q+1)

divisible

n + 4 = 3q + 1 + 4 = 3q + 5,

not divisible.

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