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For any positive integer n, show that one and only one out of n, n+3, n+6, or n+9 is divisible by 4.
Dear Palak n can be of the form of i) 4nii) 4n + 1iii) 4n + 2iv) 4n + 3 Now using 1st case4n, 4n+ 3, 4n + 6 , 4n + 9Only 4n is divisible by 4 Now using 2nd case4n + 1, 4n + 4, 4n + 7, 4n + 10Only 4n + 4 = 4 (n+1) is divisible by 4 similarly you can do this for rest of the cases and find that only one number is divisible by 4 RegardsArun (askIITians forum expert)
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