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Problems
Contests
National and Regional Contests
China Contests
China Girls Math Olympiad
2021 China Girls Math Olympiad
5
5
Part of
2021 China Girls Math Olympiad
Problems
(1)
CGMO 2021 P5
Source: CGMO 2021 P5
8/14/2021
Proof that if
4
4
4
numbers (not necessarily distinct) are picked from
{
1
,
2
,
⋯
,
20
}
\{1, 2, \cdots, 20\}
{
1
,
2
,
⋯
,
20
}
, one can pick
3
3
3
numbers among them and can label these
3
3
3
as
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
a
x
≡
b
(
m
o
d
c
)
ax \equiv b \;(\bmod\; c)
a
x
≡
b
(
mod
c
)
has integral solutions.
number theory
Diophantine equation