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Baltic Way
2014 Baltic Way
17
Equation on rationals
Equation on rationals
Source: Baltic Way 2014, Problem 17
November 11, 2014
number theory proposed
number theory
Problem Statement
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
?
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