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Nigeria Contests
2024 Nigerian MO Round 3
Problem 1
Problem 1
Part of
2024 Nigerian MO Round 3
Problems
(1)
long modular arithmetic
Source: 2024 Nigerian MO Senior Round 3 P1
4/28/2024
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
algebra
mod
number theory
modular arithmetic