MathDB
Problems
Contests
National and Regional Contests
Chile Contests
Chile National Olympiad
1997 Chile National Olympiad
2
a^1 + a^2 +...+ a^n = 1 mod 10 (1997 Chile NMO P2)
a^1 + a^2 +...+ a^n = 1 mod 10 (1997 Chile NMO P2)
Source:
November 23, 2021
number theory
divisible
divides
Problem Statement
Given integers
a
>
0
a> 0
a
>
0
,
n
>
0
n> 0
n
>
0
, suppose that
a
1
+
a
2
+
.
.
.
+
a
n
≡
1
m
o
d
10
a^1 + a^2 +...+ a^n \equiv 1 \mod 10
a
1
+
a
2
+
...
+
a
n
≡
1
mod
10
. Prove that
a
≡
n
≡
1
m
o
d
10
a \equiv n \equiv 1 \mod 10
a
≡
n
≡
1
mod
10
.
Back to Problems
View on AoPS