MathDB
Problems
Contests
International Contests
IMO Shortlist
2014 IMO Shortlist
A4
IMO shortlist 2014 A4
IMO shortlist 2014 A4
Source:
July 11, 2015
function
IMO Shortlist
algebra
functional equation
IMO Shortlist 2014
Problem Statement
Determine all functions
f
:
Z
ā
Z
f: \mathbb{Z}\to\mathbb{Z}
f
:
Z
ā
Z
satisfying
f
(
f
(
m
)
+
n
)
+
f
(
m
)
=
f
(
n
)
+
f
(
3
m
)
+
2014
f\big(f(m)+n\big)+f(m)=f(n)+f(3m)+2014
f
(
f
(
m
)
+
n
)
+
f
(
m
)
=
f
(
n
)
+
f
(
3
m
)
+
2014
for all integers
m
m
m
and
n
n
n
.Proposed by Netherlands
Back to Problems
View on AoPS