MathDB
Problems
Contests
International Contests
Cono Sur Olympiad
2020 Cono Sur Olympiad
2
2
Part of
2020 Cono Sur Olympiad
Problems
(1)
b^2-4ac is not a perfect square
Source: Cono Sur Math Olympiad 2020 #2
12/3/2020
Given
2021
2021
2021
distinct positive integers non divisible by
2
1010
2^{1010}
2
1010
, show that it's always possible to choose
3
3
3
of them
a
a
a
,
b
b
b
and
c
c
c
, such that
∣
b
2
−
4
a
c
∣
|b^2-4ac|
∣
b
2
−
4
a
c
∣
is not a perfect square.
number theory
combinatorics
pigeonhole principle