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Olympiad
Medium
Number Theory
10–12
What is the remainder when
3
47
3^{47}
3
47
is divided by
23
23
23
?
Qual é o resto da divisão de
3
47
3^{47}
3
47
por
23
23
23
?
Answer options
A.
9
B.
3
C.
1
D.
4
Check Answer
Solution
Step 1 of 3
1.
23
23
23
is prime and
23
∤
3
23 \nmid 3
23
∤
3
, so Fermat's little theorem gives
3
22
≡
1
(
m
o
d
23
)
3^{22} \equiv 1 \pmod{23}
3
22
≡
1
(
mod
23
)
.
Next step
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