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2017 Pakistan TST
Problem 3
Problem 3
Part of
2017 Pakistan TST
Problems
(1)
Beautiful Disguised Functional!
Source: Pakistan TST(2). P3. Proposed by Awais Chisti and Sualeh Asif
1/28/2017
Find all
f
:
R
+
→
R
+
f:\mathbb{R}^+ \rightarrow \mathbb{R}^+
f
:
R
+
→
R
+
such that for all distinct
x
,
y
,
z
x,y,z
x
,
y
,
z
f
(
x
)
2
−
f
(
y
)
f
(
z
)
=
f
(
x
y
)
f
(
y
)
f
(
z
)
[
f
(
y
z
)
−
f
(
z
x
)
]
f(x)^2-f(y)f(z)=f(x^y)f(y)f(z)[f(y^z)-f(z^x)]
f
(
x
)
2
−
f
(
y
)
f
(
z
)
=
f
(
x
y
)
f
(
y
)
f
(
z
)
[
f
(
y
z
)
−
f
(
z
x
)]
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