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Laurențiu Panaitopol, Tulcea
2010 Laurențiu Panaitopol, Tulcea
2
Injective, but not surjective
Injective, but not surjective
Source: Gazeta matematică
October 28, 2019
function
floor function
algebra
quadratic integers
Problem Statement
Let be a nonnegative integer
n
n
n
such that
n
\sqrt n
n
is not integer. Show that the function
f
:
{
a
+
b
n
∣
a
,
b
∈
{
0
}
∪
N
,
a
2
−
n
b
2
=
1
}
⟶
{
0
}
∪
N
,
f
(
x
)
=
⌊
x
⌋
f:\{ a+b\sqrt n | a,b\in\{ 0\}\cup\mathbb{N} , a^2-nb^2=1 \}\longrightarrow\{ 0\}\cup\mathbb{N} , f(x) =\lfloor x \rfloor
f
:
{
a
+
b
n
∣
a
,
b
∈
{
0
}
∪
N
,
a
2
−
n
b
2
=
1
}
⟶
{
0
}
∪
N
,
f
(
x
)
=
⌊
x
⌋
is injective and non-surjective.
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