Prove the following by using the principle of mathematical induction for all `n in N`:`41^n-14^n`is a multiple of 27.

Explanation

Let the given statement be `P(n)`, i.e.,
`P(n): 41^n−14^n` is a multiple of 27.


It can be observed that P(n) is true for `n = 1` since
`41^1−14^1=27`


, which is a multiple of 27.
Let P (k) be true for some positive integer k, i.e.,
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