Question 618978
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Hi,
Show that one and only one out of <u> n, n+2 and n+4</u> is divisible by 3, where ‘n’ is any positive integer.
By the Division Algorithm, n is either of the form 3k, 3k + 1, or 3k + 2.
3k: {{{highlight(3k)}}},3k+2,3k+4
3k+1: 3k+1, {{{highlight(3k+3)}}}, 3k+5
3k+2: 3k+2, +3k+4,{{{highlight(3k+6)}}}
In either of the allowed forms, there is only one of<u> n, n+2 and n+4</u> divisible by three