MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1989 All Soviet Union Mathematical Olympiad
509
ASU 509 All Soviet Union MO 1989 f(n+1) = f( f(n) ) + f( f(n+2) )
ASU 509 All Soviet Union MO 1989 f(n+1) = f( f(n) ) + f( f(n+2) )
Source:
August 14, 2019
functional
functional equation
Problem Statement
N
N
N
is the set of positive integers. Does there exist a function
f
:
N
ā
N
f: N \to N
f
:
N
ā
N
such that
f
(
n
+
1
)
=
f
(
f
(
n
)
)
+
f
(
f
(
n
+
2
)
)
f(n+1) = f( f(n) ) + f( f(n+2) )
f
(
n
+
1
)
=
f
(
f
(
n
))
+
f
(
f
(
n
+
2
))
for all
n
n
n
?
Back to Problems
View on AoPS