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2019 CIIM
Problem 6
CIIM 2019 Problem 6
CIIM 2019 Problem 6
Source:
August 30, 2021
CIIM
function
Problem Statement
Determine all the injective functions
f
:
Z
+
→
Z
+
f : \mathbb{Z}_+ \to \mathbb{Z}_+
f
:
Z
+
→
Z
+
, such that for each pair of integers
(
m
,
n
)
(m, n)
(
m
,
n
)
the following conditions hold:
a
)
a)
a
)
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn) = f(m)f(n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
b
)
b)
b
)
f(m^2 + n^2) \mid f(m^2) + f(n^2).
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