72n – 32n is divisible by 4. – InterviewSolution

1.

72n – 32n is divisible by 4.

Answer»

Let P(n): 7ⁿ – 3ⁿ is divisible by 4.

For n = 1, P(1): 71 – 31 = 4 which is divisible by 4.

∴ P(1) is true.

Let us assume P(k) is true for some k∈N

i.e., 7²ⁿ – 3²ⁿ is divisible by 4.

Thus, P(k) ⇒ P(k +1).

Hence, by mathematical induction P(n) is true for all n∈N

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