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1962 All Russian Mathematical Olympiad
024
ASU 024 All Russian MO 1962 10.3 (x-y)^5+(y-z)^5+(z-x)^5
ASU 024 All Russian MO 1962 10.3 (x-y)^5+(y-z)^5+(z-x)^5
Source:
June 17, 2019
polynomial
number theory
algebra
Problem Statement
Given
x
,
y
,
z
x,y,z
x
,
y
,
z
, three different integers. 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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