Question 620766
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Hi,
Show that one and only one out of n, n+2, n+4 is divisible by 3, where n is any positive integer
Note: number {{{highlight(n)}}}must leave a remainder of either 0, 2, or 4 when divided by 3, 
so it can be written as either 3k, 3k+2, or 3k+4 for some k (the quotient). 
If n = 3k: {{{highlight(3k)}}}, 3k + 2, 3k + 4
If n = 3k+2:  3k+2, 3k + 4, {{{highlight(3k+6)}}}
If n = 3k+4:  3k+4, {{{highlight(3k+6)}}}, 3k + 8
In each case, one and only one out of n, n+2, n+4 is divisible by 3