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KoMaL A Problems 2019/2020
A. 765
So Many Terms
So Many Terms
Source: KöMaL A. 765
March 20, 2022
algebra
functional equation
komal
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
which satisfy the following equality for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
f
(
x
)
f
(
y
)
−
f
(
x
−
1
)
−
f
(
y
+
1
)
=
f
(
x
y
)
+
2
x
−
2
y
−
4.
f(x)f(y)-f(x-1)-f(y+1)=f(xy)+2x-2y-4.
f
(
x
)
f
(
y
)
−
f
(
x
−
1
)
−
f
(
y
+
1
)
=
f
(
x
y
)
+
2
x
−
2
y
−
4.
Proposed by Dániel Dobák, Budapest
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