MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2016 Canadian Mathematical Olympiad Qualification
1
11 and 31 divides sums of powers
11 and 31 divides sums of powers
Source: Canada Repêchage 2016/1
June 19, 2016
number theory
Problem Statement
(a) Find all positive integers
n
n
n
such that
11
∣
(
3
n
+
4
n
)
11|(3^n + 4^n)
11∣
(
3
n
+
4
n
)
.(b) Find all positive integers
n
n
n
such that
31
∣
(
4
n
+
7
n
+
2
0
n
)
31|(4^n + 7^n + 20^n)
31∣
(
4
n
+
7
n
+
2
0
n
)
.
Back to Problems
View on AoPS