Prove that only one of the numbers n -1, n + 1 or n + 3 is divisible by 3 ,Where n is any positive
integer .
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On dividing n by 3, let q be the quotient and r be the remainder . Case I If n = 3q then n is clearly divisible by 3. Case II If n= ( 3q +1) then ( n+2) = (3q +3) = 3(q +1) , which is clearly divisible by 3. ... Hence, one and only one out of n,( n +1) and (n+2) is divisible by 3.
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