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

MCQ

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

A
26
✓
24
C
11
D
25

✓

Answer

Correct option: B.

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

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