InterviewSolution
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InterviewSolution
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For any positive integer m ______ is divisible by 4.(a) 5m^2 + 2(b) 3m + 1(c) m^2 + 3(d) m^3 + 3mI had been asked this question during an interview.I want to ask this question from Principle of Mathematical Induction topic in division Induction and Recursion of Discrete Mathematics |
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Answer» RIGHT ANSWER is (d) m^3 + 3m Best explanation: The required answer is, m^3 + 3m. Now, by INDUCTION hypothesis, we have to prove for m=K, k^3+3k is divisible by 4. So, (k + 1)^3 + 3 (k + 1) = k^3 + 3 k^2 + 6 k + 4 = [k^3 + 3 k] + [3 k^2 + 3 k + 4] = 4M + (12k^2 + 12k) – (8K^2 + 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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