For any natural number n, 7^n – 2^n is divisible by - Vidyadip

MCQ

For any natural number $n, 7^n – 2^n$ is divisible by

A
$3$
B
$4$
✓
$5$
D
$7$

✓

Answer

Correct option: C.

$5$

Given, $ 7^n – 2^n $
Let $n = 1$
$7^n – 2^n$
$= 7^1 – 2^1$
$= 7 – 2$
$= 5 $
which is divisible by $5$
Let $n = 2$
$ 7^n – 2^n$
$= 72 – 22$
$= 49 – 4$
$= 45$
which is divisible by $5$
Let $n = 3$
$ 7^n – 2^n$
$= 7^3 – 2^3$
$= 343 – 8$
$= 335$
which is divisible by $5$
Hence, for any natural number $n, 7^n – 2^n $ is divisible by $5$

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