Prove the following by the principle of mathematical induction: `3^(2n)+7` is divisible by 8 for all `n in Ndot`

Explanation

Suppose P (n): `3^(2n )`+ 7 is divisible by 8

Now let us check for n = 1,

P (1): `3^2` + 7 = 9 + 7 = 16

P (n) is true for n = 1. Where, P (n) is divisible by 8
Then, let us check for P (n) is true for n = k, and have to prove that P (k + 1) is true.
P (k): `3^(2k )`+ 7 is divisible by 8

: `3^(2k)` + 7 = 8λ

: `3^(2k)` = 8λ – 7 … (i)

Now we have to prove,
`3^(2(k + 1) `+ 7 is divisible by 8

`3^(2k)` + 2 + 7 = 8μ
Therefore,
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