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International Contests
International Zhautykov Olympiad
2018 International Zhautykov Olympiad
5
5
Part of
2018 International Zhautykov Olympiad
Problems
(1)
izho2018 P5 (algebra)
Source: izho2018
2/14/2018
Find all real numbers
a
a
a
such that there exist
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
with
f
(
x
−
f
(
y
)
)
=
f
(
x
)
+
a
[
y
]
f(x-f(y))=f(x)+a[y]
f
(
x
−
f
(
y
))
=
f
(
x
)
+
a
[
y
]
for all
x
,
y
∈
R
x,y\in \mathbb{R}
x
,
y
∈
R
inequalities
algebra
function
floor function