MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
2017 Poland - Second Round
6
Perfect square
Perfect square
Source: Polish MO
February 25, 2017
number theory
prime numbers
Problem Statement
A prime number
p
>
2
p > 2
p
>
2
and
x
,
y
∈
{
1
,
2
,
…
,
p
−
1
2
}
x,y \in \left\{ 1,2,\ldots, \frac{p-1}{2} \right\}
x
,
y
∈
{
1
,
2
,
…
,
2
p
−
1
}
are given. Prove that if
x
(
p
−
x
)
y
(
p
−
y
)
x\left( p-x\right)y\left( p-y\right)
x
(
p
−
x
)
y
(
p
−
y
)
is a perfect square, then
x
=
y
x = y
x
=
y
.
Back to Problems
View on AoPS