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UPSC CDS 1 2021 Math Paper
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© examsnet.com
Question : 4
Total: 100
If
n
is any natural number, then
5
2
n
−
1
is always divisible by how many natural numbers?
1
4
6
8
Validate
Solution:
👈: Video Solution
let
n
=
1
then
5
2
|
−
1
=
5
2
−
1
=
24
n
=
2
then
5
4
−
1
=
(
5
2
−
1
)
(
5
2
+
1
)
=
24
(
5
2
−
1
)
n
=
3
then
5
6
−
1
=
(
5
2
−
1
)
(
5
4
+
5
2
+
1
)
=
24
(
5
4
+
5
2
+
1
)
we can observe that we get always factor of 24 and factors of 24 are
1
,
2
,
3
,
4
,
6
,
8
,
12
,
24
.
So, number of natural numbers that divides
5
2
n
−
1
are 8 .
© examsnet.com
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