MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2016 Canadian Mathematical Olympiad Qualification
1
1
Part of
2016 Canadian Mathematical Olympiad Qualification
Problems
(1)
11 and 31 divides sums of powers
Source: Canada Repêchage 2016/1
6/19/2016
(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
)
.
number theory