Mixing
Number theory: Unit group of ring of integer of number field
1
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Somebody can help me proof the unit group of ring of integer of 5th cyclotomic field is infinite
abstract-algebra number-theory
edited Jan 16 at 9:04
Bernard
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
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add a comment |
1
$begingroup$
Somebody can help me proof the unit group of ring of integer of 5th cyclotomic field is infinite
abstract-algebra number-theory
edited Jan 16 at 9:04
Bernard
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
$endgroup$
$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16
add a comment |
1
1
1
$begingroup$
Somebody can help me proof the unit group of ring of integer of 5th cyclotomic field is infinite
abstract-algebra number-theory
edited Jan 16 at 9:04
Bernard
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
$endgroup$
Somebody can help me proof the unit group of ring of integer of 5th cyclotomic field is infinite
abstract-algebra number-theory
abstract-algebra number-theory
edited Jan 16 at 9:04
Bernard
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
edited Jan 16 at 9:04
Bernard
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
edited Jan 16 at 9:04
Bernard
121k740116
edited Jan 16 at 9:04
Bernard
121k740116
edited Jan 16 at 9:04
Bernard
121k740116
121k740116
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
asked Jan 16 at 7:36
LeHoaiNamLeHoaiNam
62
62
$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16
add a comment |
$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16
$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16
$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16
add a comment |
1 Answer
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Can you prove that $Bbb Q(zeta_5)$ contains $Bbb Q(sqrt5)$?
And can you prove that the integer ring of $Bbb Q(sqrt5)$ has infinitely
many units?
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
$endgroup$
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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active
oldest
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active
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2
$begingroup$
Can you prove that $Bbb Q(zeta_5)$ contains $Bbb Q(sqrt5)$?
And can you prove that the integer ring of $Bbb Q(sqrt5)$ has infinitely
many units?
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
$endgroup$
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
add a comment |
2
$begingroup$
Can you prove that $Bbb Q(zeta_5)$ contains $Bbb Q(sqrt5)$?
And can you prove that the integer ring of $Bbb Q(sqrt5)$ has infinitely
many units?
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
$endgroup$
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
add a comment |
2
2
2
$begingroup$
Can you prove that $Bbb Q(zeta_5)$ contains $Bbb Q(sqrt5)$?
And can you prove that the integer ring of $Bbb Q(sqrt5)$ has infinitely
many units?
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
$endgroup$
Can you prove that $Bbb Q(zeta_5)$ contains $Bbb Q(sqrt5)$?
And can you prove that the integer ring of $Bbb Q(sqrt5)$ has infinitely
many units?
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
answered Jan 16 at 7:47
Lord Shark the UnknownLord Shark the Unknown
105k1160132
105k1160132
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
add a comment |
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
$begingroup$
I'm not sure. I'm reading " Number theory and fermat's last theory" (Ivan Stewart) and doing exercise 5 subsection 3.3 page 72. I can't solve it by the way that author gave! Can you show me more detail, sir!
$endgroup$
– LeHoaiNam
Jan 16 at 8:06
add a comment |
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$begingroup$
What is the inverse of $a+b sqrt{5} in mathbb{Z}[ sqrt{5}]$, when is it a unit en.wikipedia.org/wiki/Pell%27s_equation
$endgroup$
– reuns
Jan 16 at 11:16