MathDB
Problems
Contests
National and Regional Contests
China Contests
China Northern MO
2017 China Northern MO
2
2
Part of
2017 China Northern MO
Problems
(1)
China Northern Mathematical Olympiad 2017, Problem 2
Source: China Northern Mathematical Olympiad 2017
7/29/2017
Prove that there exist infinitely many integers
n
n
n
which satisfy
201
7
2
∣
1
n
+
2
n
+
.
.
.
+
201
7
n
2017^2 | 1^n + 2^n + ... + 2017^n
201
7
2
∣
1
n
+
2
n
+
...
+
201
7
n
.
Divisibility
number theory