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Dutch IMO TST
2020 Dutch IMO TST
3
f( - f (x) - f (y))= 1 -x - y , in Zxz
f( - f (x) - f (y))= 1 -x - y , in Zxz
Source: 2020 Dutch IMO TST 3.3
November 22, 2020
functional equation
functional equation in Z
functional
algebra
Problem Statement
Find all functions
f
:
Z
→
Z
f: Z \to Z
f
:
Z
→
Z
that satisfy
f
(
−
f
(
x
)
−
f
(
y
)
)
=
1
−
x
−
y
f(-f (x) - f (y))= 1 -x - y
f
(
−
f
(
x
)
−
f
(
y
))
=
1
−
x
−
y
for all
x
,
y
∈
Z
x, y \in Z
x
,
y
∈
Z
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