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Turkey Olympic Revenge
2023 Turkey Olympic Revenge
1
1
Part of
2023 Turkey Olympic Revenge
Problems
(1)
Non-Standard Functional Equation ft. Real Number c
Source: Turkey Olympic Revenge 2023 P1
3/6/2023
Find all
c
∈
R
c\in \mathbb{R}
c
∈
R
such that there exists a function
f
:
R
→
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
→
R
satisfying
(
f
(
x
)
+
1
)
(
f
(
y
)
+
1
)
=
f
(
x
+
y
)
+
f
(
x
y
+
c
)
(f(x)+1)(f(y)+1)=f(x+y)+f(xy+c)
(
f
(
x
)
+
1
)
(
f
(
y
)
+
1
)
=
f
(
x
+
y
)
+
f
(
x
y
+
c
)
for all
x
,
y
∈
R
x,y\in \mathbb{R}
x
,
y
∈
R
.Proposed by Kaan Bilge
functional equation
function
function in R
olympic revenge
algebra