MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2024 India IMOTC
9
9
Part of
2024 India IMOTC
Problems
(1)
Cute FE, but you all get 0
Source: India IMOTC 2024 Day 3 Problem 3
5/31/2024
Find all functions
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that for all real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
, we have
f
(
a
+
b
+
c
)
f
(
a
b
+
b
c
+
c
a
)
−
f
(
a
)
f
(
b
)
f
(
c
)
=
f
(
a
+
b
)
f
(
b
+
c
)
f
(
c
+
a
)
.
f(a+b+c)f(ab+bc+ca) - f(a)f(b)f(c) = f(a+b)f(b+c)f(c+a).
f
(
a
+
b
+
c
)
f
(
ab
+
b
c
+
c
a
)
−
f
(
a
)
f
(
b
)
f
(
c
)
=
f
(
a
+
b
)
f
(
b
+
c
)
f
(
c
+
a
)
.
Proposed by Mainak Ghosh and Rijul Saini
functional equation
algebra