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National and Regional Contests
PEN Problems
PEN F Problems
16
16
Part of
PEN F Problems
Problems
(1)
F 16
Source:
5/25/2007
Prove that for any distinct rational numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
, the number
1
(
b
−
c
)
2
+
1
(
c
−
a
)
2
+
1
(
a
−
b
)
2
\frac{1}{(b-c)^{2}}+\frac{1}{(c-a)^{2}}+\frac{1}{(a-b)^{2}}
(
b
−
c
)
2
1
+
(
c
−
a
)
2
1
+
(
a
−
b
)
2
1
is the square of some rational number.
rational numbers