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Byju's Answer
Standard VII
Mathematics
Integers
If n is a nat...
Question
If n is a natural number then 9
2n
– 5
2n
is divisible by --
Open in App
Solution
Dear Student
G
i
v
e
n
9
2
n
-
5
2
n
=
9
2
n
-
5
2
n
=
9
n
2
-
5
n
2
=
9
n
+
5
n
9
n
-
5
n
∵
a
2
-
b
2
=
a
+
b
a
-
b
N
o
w
w
h
e
n
n
i
s
e
v
e
n
t
h
e
n
t
h
e
s
e
c
o
n
d
t
e
r
m
w
i
l
l
h
a
v
e
f
a
c
t
o
r
s
(
9
+
5
)
a
n
d
(
9
-
5
)
=
14
a
n
d
4
s
o
,
2
a
n
d
7
a
r
e
t
h
e
f
a
c
t
o
r
s
N
o
w
w
h
e
n
n
i
s
o
d
d
t
h
e
f
i
r
s
t
t
e
r
m
w
i
l
l
h
a
v
e
f
a
c
t
o
r
(
9
+
5
)
=
14
a
n
d
s
e
c
o
n
d
t
e
r
m
w
i
l
l
h
a
v
e
f
a
c
t
o
r
(
9
-
5
)
=
4
s
o
,
2
a
n
d
7
a
r
e
t
h
e
f
a
c
t
o
r
s
∴
9
2
n
-
5
2
n
i
s
d
i
v
i
s
i
b
l
e
b
y
2
a
n
d
7
Regards
Suggest Corrections
2
Similar questions
Q.
If
n
is a natural number the
9
2
n
−
4
2
n
is always divisible by :
Q.
If n is a natural number, then 9
2n
− 4
2n
is always divisible by
(a) 5
(b) 13
(c) both 5 and 13
(d) None of these
[Hint : 9
2n
− 4
2n
is of the form a
2n
− b
2n
which is divisible by both a − b and a + b. So, 9
2n
− 4
2n
is divisible by both 9 − 4 = 5 and 9 + 4 = 13.]
