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Baltic Way
1994 Baltic Way
1
a∘b is defined as a+b-ab
a∘b is defined as a+b-ab
Source: Baltic Way 1994
December 22, 2011
algebra proposed
algebra
Problem Statement
Let
a
∘
b
=
a
+
b
−
a
b
a\circ b=a+b-ab
a
∘
b
=
a
+
b
−
ab
. Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of integers such that
(
x
∘
y
)
∘
z
+
(
y
∘
z
)
∘
x
+
(
z
∘
x
)
∘
y
=
0
(x\circ y)\circ z +(y\circ z)\circ x +(z\circ x)\circ y=0
(
x
∘
y
)
∘
z
+
(
y
∘
z
)
∘
x
+
(
z
∘
x
)
∘
y
=
0
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