For all n N, 5^ 2n − 1 is divisible by:

MCQ

For all $n\in N, 5^{2n}− 1$ is divisible by:

A
$26$
✓
$24$
C
$11$
D
$25$

✓

Answer

Correct option: B.

$24$

Given number $= 5^{2n}− 1$
Let $n = 1, 2, 3, 4, ……..$
$ 5^{2 n}-1=5^2-1=25-1=24 $
$ 5^{2 n}-1=5^4-1=625-1=624=24 \times 26 $
$ 5^{2 n}-1=5^6-1=15625-1=15624=651 \times 24 $
Since, all these numbers are divisible by $24$ for $n = 1, 2, 3, …..$
So, the given number is divisible by $2$

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