show that one and only one out of n,n+2or n+4 is divisible by 3 ,where n is any positive integers
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n+2 = 3q+2+2 =3q+4 = 3(q+1)+1 is not divisible by 3. n+4 = 3q+2+4 = 3q+6 = 3(q+2) is divisible by 3. Thus one and only one out of n , n+2, n+4 is divisible by 3.
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