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Canadian Mathematical Olympiad Qualification Repechage
2016 Canadian Mathematical Olympiad Qualification
6
GCD greater than GCD
GCD greater than GCD
Source: Canada Repêchage 2016/6
June 19, 2016
number theory
greatest common divisor
Problem Statement
Determine all ordered triples of positive integers
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
such that
gcd
(
x
+
y
,
y
+
z
,
z
+
x
)
>
gcd
(
x
,
y
,
z
)
\gcd(x+y, y+z, z+x) > \gcd(x, y, z)
g
cd
(
x
+
y
,
y
+
z
,
z
+
x
)
>
g
cd
(
x
,
y
,
z
)
.
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