MathDB
Problems
Contests
International Contests
Baltic Way
2014 Baltic Way
17
17
Part of
2014 Baltic Way
Problems
(1)
Equation on rationals
Source: Baltic Way 2014, Problem 17
11/11/2014
Do there exist pairwise distinct rational numbers
x
,
y
x, y
x
,
y
and
z
z
z
such that
1
(
x
−
y
)
2
+
1
(
y
−
z
)
2
+
1
(
z
−
x
)
2
=
2014
?
\frac{1}{(x - y)^2}+\frac{1}{(y - z)^2}+\frac{1}{(z - x)^2}= 2014?
(
x
−
y
)
2
1
+
(
y
−
z
)
2
1
+
(
z
−
x
)
2
1
=
2014
?
number theory proposed
number theory