MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2009 Dutch IMO TST
4
f : Z \to Z, f(m + n) + f(mn - 1) = f(m)f(n) + 2
f : Z \to Z, f(m + n) + f(mn - 1) = f(m)f(n) + 2
Source: 2009 Dutch IMO TST P4
January 10, 2020
functional equation
functional equation in Z
algebra
Problem Statement
Find all functions
f
:
Z
→
Z
f : Z \to Z
f
:
Z
→
Z
satisfying
f
(
m
+
n
)
+
f
(
m
n
−
1
)
=
f
(
m
)
f
(
n
)
+
2
f(m + n) + f(mn -1) = f(m)f(n) + 2
f
(
m
+
n
)
+
f
(
mn
−
1
)
=
f
(
m
)
f
(
n
)
+
2
for all
m
,
n
∈
Z
m, n \in Z
m
,
n
∈
Z
.
Back to Problems
View on AoPS