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National and Regional Contests
PEN Problems
PEN K Problems
22
22
Part of
PEN K Problems
Problems
(1)
K 22
Source:
5/25/2007
Find all functions
f
:
Q
+
→
Q
+
f:\mathbb{Q}^{+} \to \mathbb{Q}^{+}
f
:
Q
+
→
Q
+
such that for all
x
∈
Q
+
x\in \mathbb{Q}^+
x
∈
Q
+
: [*]
f
(
x
+
1
)
=
f
(
x
)
+
1
f(x+1)=f(x)+1
f
(
x
+
1
)
=
f
(
x
)
+
1
, [*]
f
(
x
2
)
=
f
(
x
)
2
f(x^2)=f(x)^2
f
(
x
2
)
=
f
(
x
)
2
.
function
induction
Functional Equations