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India National Olympiad
1994 India National Olympiad
6
Another func eq!!
Another func eq!!
Source: INMO 1994 Problem 6
October 6, 2005
function
continued fraction
algebra unsolved
algebra
Problem Statement
Find all real-valued functions
f
f
f
on the reals such that
f
(
−
x
)
=
−
f
(
x
)
f(-x) = -f(x)
f
(
−
x
)
=
−
f
(
x
)
,
f
(
x
+
1
)
=
f
(
x
)
+
1
f(x+1) = f(x) + 1
f
(
x
+
1
)
=
f
(
x
)
+
1
for all
x
x
x
, and
f
(
1
x
)
=
f
(
x
)
x
2
f\left(\dfrac{1}{x}\right) = \dfrac{f(x)}{x^2}
f
(
x
1
)
=
x
2
f
(
x
)
for
x
≠
0
x \not = 0
x
=
0
.
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