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IFYM Int. Fest. of Young Mathematicians, Sozopol
2015 IFYM, Sozopol
3
Function R+ in R+
Function R+ in R+
Source:
May 31, 2013
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
+
⟶
R
+
f:\mathbb R^{+} \longrightarrow \mathbb R^{+}
f
:
R
+
⟶
R
+
so that
f
(
x
y
+
f
(
x
y
)
)
=
x
y
+
x
f
(
y
)
f(xy + f(x^y)) = x^y + xf(y)
f
(
x
y
+
f
(
x
y
))
=
x
y
+
x
f
(
y
)
for all positive reals
x
,
y
x,y
x
,
y
.
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