questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Binomial Theorem
Question 83
Question 83 of 347
Medium
NUMERICAL
Remainder when
64
32
32
64^{32^{32}}
6
4
3
2
32
is divided by 9 is equal to \_\_\_\_\_\_\_\_. Answer: 1
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
Let
32
32
=
t
{32}^{32}=t
32
32
=
t
64
32
32
=
64
t
=
8
2
t
=
(
9
−
1
)
2
t
=
9
k
+
1
\begin{gathered} {64}^{{32}^{32}}={64}^{t}={8}^{2t}=(9-1{)}^{2t} \\ =9k+1 \end{gathered}
64
32
32
=
64
t
=
8
2
t
=
(
9
−
1
)
2
t
=
9
k
+
1
Hence remainder
=
1
=1
=
1
Answer the question to unlock
Previous
Next