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1976 IMO Longlists
50
f(x+ 2) - f(x) = x^2 + 2x + 4
f(x+ 2) - f(x) = x^2 + 2x + 4
Source:
January 28, 2011
function
induction
floor function
algebra unsolved
algebra
Problem Statement
Find a function
f
(
x
)
f(x)
f
(
x
)
defined for all real values of
x
x
x
such that for all
x
x
x
,
f
(
x
+
2
)
−
f
(
x
)
=
x
2
+
2
x
+
4
,
f(x+ 2) - f(x) = x^2 + 2x + 4,
f
(
x
+
2
)
−
f
(
x
)
=
x
2
+
2
x
+
4
,
and if
x
∈
[
0
,
2
)
x \in [0, 2)
x
∈
[
0
,
2
)
, then
f
(
x
)
=
x
2
.
f(x) = x^2.
f
(
x
)
=
x
2
.
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