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Pan African
2010 Pan African
3
f(x+f(y))=f(x)-y
f(x+f(y))=f(x)-y
Source: Pan African Olympiad 2010
October 1, 2011
function
algebra
domain
induction
algebra proposed
Problem Statement
Does there exist a function
f
:
Z
→
Z
f:\mathbb{Z}\to\mathbb{Z}
f
:
Z
→
Z
such that
f
(
x
+
f
(
y
)
)
=
f
(
x
)
−
y
f(x+f(y))=f(x)-y
f
(
x
+
f
(
y
))
=
f
(
x
)
−
y
for all integers
x
x
x
and
y
y
y
?
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