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Problems
Contests
International Contests
APMO
2015 APMO
2
2
Part of
2015 APMO
Problems
(1)
Existence of function on a set
Source: APMO 2015 Problem 2
3/30/2015
Let
S
=
{
2
,
3
,
4
,
…
}
S = \{2, 3, 4, \ldots\}
S
=
{
2
,
3
,
4
,
…
}
denote the set of integers that are greater than or equal to
2
2
2
. Does there exist a function
f
:
S
→
S
f : S \to S
f
:
S
→
S
such that
f
(
a
)
f
(
b
)
=
f
(
a
2
b
2
)
for all
a
,
b
∈
S
with
a
≠
b
?
f (a)f (b) = f (a^2 b^2 )\text{ for all }a, b \in S\text{ with }a \ne b?
f
(
a
)
f
(
b
)
=
f
(
a
2
b
2
)
for all
a
,
b
∈
S
with
a
=
b
?
Proposed by Angelo Di Pasquale, Australia
function
algebra