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International Contests
IberoAmerican
1993 IberoAmerican
3
8th ibmo - mexico 1993/q3.
8th ibmo - mexico 1993/q3.
Source: Spanish Communities
May 7, 2006
function
algebra proposed
algebra
Problem Statement
Let
N
∗
=
{
1
,
2
,
…
}
\mathbb{N}^*=\{1,2,\ldots\}
N
∗
=
{
1
,
2
,
…
}
. Find al the functions
f
:
N
∗
→
N
∗
f: \mathbb{N}^*\rightarrow \mathbb{N}^*
f
:
N
∗
→
N
∗
such that:(1) If
x
<
y
x<y
x
<
y
then
f
(
x
)
<
f
(
y
)
f(x)<f(y)
f
(
x
)
<
f
(
y
)
. (2)
f
(
y
f
(
x
)
)
=
x
2
f
(
x
y
)
f\left(yf(x)\right)=x^2f(xy)
f
(
y
f
(
x
)
)
=
x
2
f
(
x
y
)
for all
x
,
y
∈
N
∗
x,y \in\mathbb{N}^*
x
,
y
∈
N
∗
.
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