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Byju's Answer
Standard XII
Mathematics
Permutation
Prove that ...
Question
Prove that
2
4
n
−
1
is divisible by
15
.
Open in App
Solution
2
4
n
−
1
=
(
2
4
)
n
−
1
n
=
16
n
−
1
n
a
n
−
b
n
=
(
a
−
b
)
(
a
n
−
1
+
a
n
−
2
b
+
a
n
−
3
b
2
.
.
.
.
.
.
.
.
.
.
.
b
n
−
1
)
⇒
16
n
−
1
n
=
(
16
−
1
)
(
16
n
−
1
+
16
n
−
2
.1
+
16
n
−
3
1
2
.
.
.
.
.
.
1
n
−
1
)
⇒
16
n
−
1
n
=
15
(
16
n
−
1
+
16
n
−
2
.1
+
16
n
−
3
1
2
.
.
.
.
.
.
.
.
.
.
.
1
n
−
1
)
which is clearly divisible by
15
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