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All-Russian Olympiad
1962 All-Soviet Union Olympiad
12
Three variable expression divisibility
Three variable expression divisibility
Source: 1962 All-Soviet Union Olympiad
January 15, 2018
number theory
Russia
algebra
Divisibility
Problem Statement
Given unequal integers
x
,
y
,
z
x, y, z
x
,
y
,
z
prove that
(
x
−
y
)
5
+
(
y
−
z
)
5
+
(
z
−
x
)
5
(x-y)^5 + (y-z)^5 + (z-x)^5
(
x
−
y
)
5
+
(
y
−
z
)
5
+
(
z
−
x
)
5
is divisible by
5
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
5(x-y)(y- z)(z-x)
5
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
.
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