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Singapore MO Open
2019 Singapore MO Open
2
smo 2019 open 2nd round q2
smo 2019 open 2nd round q2
Source:
August 15, 2019
functional equation
function
algebra
Problem Statement
find all functions
f
:
Z
→
Z
f : \mathbb{Z} \to \mathbb{Z}
f
:
Z
→
Z
such that
f
(
−
f
(
x
)
−
f
(
y
)
)
=
1
−
x
−
y
f(-f(x)-f(y)) = 1-x-y
f
(
−
f
(
x
)
−
f
(
y
))
=
1
−
x
−
y
\forall x,y \in \mathbb{Z}
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