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For any positive integer m ______ is divisible by 4.

For any positive integer m ______ is divisible by 4. Correct Answer m3 + 3m

The required answer is, m3 + 3m. Now, by induction hypothesis, we have to prove for m=k, k3+3k is divisible by 4. So, (k + 1)3 + 3 (k + 1) = k3 + 3 k2 + 6 k + 4 = + = 4M + (12k2 + 12k) – (8k2 + 8k – 4), both the terms are divisible by 4. Hence (k + 1)3 + 3 (k + 1) is also divisible by 4 and hence it is proved for any integer m.

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