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National and Regional Contests
Nigeria Contests
2024 Nigerian MO Round 3
Problem 1
long modular arithmetic
long modular arithmetic
Source: 2024 Nigerian MO Senior Round 3 P1
April 28, 2024
algebra
mod
number theory
modular arithmetic
Problem Statement
Find the value of
(
2
40
+
1
2
41
+
2
3
42
+
6
7
43
+
8
7
44
)
45
!
+
46
m
o
d
11
(2^{40}+12^{41}+23^{42}+67^{43}+87^{44})^{45!+46}\mod11
(
2
40
+
1
2
41
+
2
3
42
+
6
7
43
+
8
7
44
)
45
!
+
46
mod
11
(variation but same answer) 3
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