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National and Regional Contests
Greece Contests
Greece National Olympiad
1987 Greece National Olympiad
2
f(x)+f(x+1)+f(x+2)+...+f(x+1986)=0 1987 Greece MO Grade XI p2
f(x)+f(x+1)+f(x+2)+...+f(x+1986)=0 1987 Greece MO Grade XI p2
Source:
September 6, 2024
function
periodic
periodic function
Problem Statement
If for function
f
f
f
holds that
f
(
x
)
+
f
(
x
+
1
)
+
f
(
x
+
2
)
+
.
.
.
+
f
(
x
+
1986
)
=
0
f(x)+f(x+1)+f(x+2)+...+f(x+1986)=0
f
(
x
)
+
f
(
x
+
1
)
+
f
(
x
+
2
)
+
...
+
f
(
x
+
1986
)
=
0
for any
ā
R
\in\mathbb{R}
ā
R
, prove that
f
f
f
is periodic and find one period of her.
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