SOLUTION: Show that one and only one out of n, n+2 and n+4 is divisible by 3, where �n� is any positive integer.

SOLUTION: Show that one and only one out of n, n+2 and n+4 is divisible by 3, where �n� is any positive integer.

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Question 618975: Show that one and only one out of n, n+2 and n+4 is divisible by 3, where �n� is any positive integer.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Consider this in terms of modulo 3. n+4 is equivalent to n+1 (mod 3), so we have to show that out of n, n+2, n+1, only one of them is divisible by 3. Here, it's just simple casework based on n ≡ 0, 1, 2 (mod 3). There will always be exactly one integer of those three that is divisible by 3.
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