MathDB
Problems
Contests
National and Regional Contests
China Contests
China National Olympiad
2022 China National Olympiad
3
3
Part of
2022 China National Olympiad
Problems
(1)
ax+y ranges mod 37
Source: CMO 2022 P3
12/21/2021
Find all positive integers
a
a
a
such that there exists a set
X
X
X
of
6
6
6
integers satisfying the following conditions: for every
k
=
1
,
2
,
…
,
36
k=1,2,\ldots ,36
k
=
1
,
2
,
…
,
36
there exist
x
,
y
∈
X
x,y\in X
x
,
y
∈
X
such that
a
x
+
y
−
k
ax+y-k
a
x
+
y
−
k
is divisible by
37
37
37
.
number theory