If n is the positive integer, then 23n - 7n - 1 is divisible by. - Vidyadip

MCQ

If n is the positive integer, then 2³ⁿ - 7n - 1 is divisible by.

A
7
B
10
C
49
D
81

✓

Answer

49

Solution:

Given: 2³ⁿ - 7n - 1. It can also be written as 8ⁿ - 7n - 1

Let 8ⁿ - 7n - 1 = 0

So, 8ⁿ = 7n + 1

8ⁿ = (1 + 7)ⁿ

By applying binomial theorem, we get

8n - 1 - 7n = 49 (or) 2³ⁿ - 7n - 1 = 49

Hence, 2³ⁿ - 7n - 1 is divisible by 49.

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