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Balkan MO
1991 Balkan MO
4
prove there isn't any bijection
prove there isn't any bijection
Source: bmo 1991
April 23, 2007
function
algebra proposed
algebra
Problem Statement
Prove that there is no bijective function
f
:
{
1
,
2
,
3
,
…
}
→
{
0
,
1
,
2
,
3
,
…
}
f : \left\{1,2,3,\ldots \right\}\rightarrow \left\{0,1,2,3,\ldots \right\}
f
:
{
1
,
2
,
3
,
…
}
→
{
0
,
1
,
2
,
3
,
…
}
such that
f
(
m
n
)
=
f
(
m
)
+
f
(
n
)
+
3
f
(
m
)
f
(
n
)
f(mn)=f(m)+f(n)+3f(m)f(n)
f
(
mn
)
=
f
(
m
)
+
f
(
n
)
+
3
f
(
m
)
f
(
n
)
.
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