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Joint Entrance Examination
Mathematics
Binomial Theorem
Question 146
Question 146 of 347
Easy
MCQ
The remainder when
3
2022
3^{2022}
3
2022
is divided by 5 is:
A
1
B
2
C
3
D
4
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Solutions · 1
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Official solution
3
4
=
81
≡
1
(
m
o
d
5
)
3^4=81\equiv1\pmod5
3
4
=
81
≡
1
(
mod
5
)
, and
2022
=
4
×
505
+
2
2022=4\times505+2
2022
=
4
×
505
+
2
, so
3
2022
≡
3
2
=
9
≡
4
(
m
o
d
5
)
3^{2022}\equiv3^2=9\equiv4\pmod5
3
2022
≡
3
2
=
9
≡
4
(
mod
5
)
. Remainder = 4
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