Show that exactly one of the numbers n,n+2,n+4 is divisible by 3.
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Solution
Case I: If n=3q n+4=3q+4n+2=3q+2 here n is only divisible by 3 Case II: If n=3q+1 n+4=3q+5n+2=3q+3=3(q+1) Here only n+2 is divisible by 3 Case III: If n=3q+2 n+2=3q+4
n+4=3q+2+4=3q+6 Here only n+4 is divisible by 3
Hence, only one of the numbers n,n+2,n+4 is divisible by 3.