MathDB
Problems
Contests
International Contests
Baltic Way
2003 Baltic Way
1
1
Part of
2003 Baltic Way
Problems
(1)
Function over the rationals
Source: Baltic Way 2003
11/5/2010
Find all functions
f
:
Q
+
→
Q
+
f:\mathbb{Q}^{+}\rightarrow \mathbb{Q}^{+}
f
:
Q
+
→
Q
+
which for all
x
∈
Q
+
x \in \mathbb{Q}^{+}
x
∈
Q
+
fulfil
f
(
1
x
)
=
f
(
x
)
and
(
1
+
1
x
)
f
(
x
)
=
f
(
x
+
1
)
.
f\left(\frac{1}{x}\right)=f(x) \ \ \text{and} \ \ \left(1+\frac{1}{x}\right)f(x)=f(x+1).
f
(
x
1
)
=
f
(
x
)
and
(
1
+
x
1
)
f
(
x
)
=
f
(
x
+
1
)
.
function
continued fraction
algebra unsolved
algebra