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1997 Tournament Of Towns
(558) 3
TOT 558 1997 Autumn S O3 xy(x -y) + yz(y-z) + zx(z-x) = 6
TOT 558 1997 Autumn S O3 xy(x -y) + yz(y-z) + zx(z-x) = 6
Source:
September 11, 2024
number theory
diophantine
Diophantine equation
Problem Statement
Prove that the equation
x
y
(
x
−
y
)
+
y
z
(
y
−
z
)
+
z
x
(
z
−
x
)
=
6
xy(x -y) + yz(y-z) + zx(z-x) = 6
x
y
(
x
−
y
)
+
yz
(
y
−
z
)
+
z
x
(
z
−
x
)
=
6
has infinitely many solutions in integers
x
,
y
x, y
x
,
y
and
z
z
z
.(N Vassiliev)
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