About associate in abstract algebra [closed] The 2019 Stack Overflow Developer Survey Results Are InHelp on abstract algebra proof?Abstract Algebra (Ring Homomorphisms and Ideals)Abstract Algebra- IdealsAbstract Algebra .. HomomorphismAbstract Algebra 1 about permutationAbstract Algebra: Showing IsomorphismThe element that is an associate of everything.Show that this field is finite and count its elementsAbstract algebra: Associate elements of irreducible and prime elementsAssociate elements in non-integral domains.

Finding the area between two curves with Integrate

Why doesn't shell automatically fix "useless use of cat"?

How to support a colleague who finds meetings extremely tiring?

Is bread bad for ducks?

What information about me do stores get via my credit card?

The phrase "to the numbers born"?

What is the meaning of Triage in Cybersec world?

Can withdrawing asylum be illegal?

What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?

Cooking pasta in a water boiler

Why not take a picture of a closer black hole?

How to obtain a position of last non-zero element

How can I add encounters in the Lost Mine of Phandelver campaign without giving PCs too much XP?

Loose spokes after only a few rides

Old scifi movie from the 50s or 60s with men in solid red uniforms who interrogate a spy from the past

How to notate time signature switching consistently every measure

Are there any other methods to apply to solving simultaneous equations?

What do hard-Brexiteers want with respect to the Irish border?

Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?

Likelihood that a superbug or lethal virus could come from a landfill

Can an undergraduate be advised by a professor who is very far away?

Does HR tell a hiring manager about salary negotiations?

Mathematics of imaging the black hole

Can there be female White Walkers?



About associate in abstract algebra [closed]



The 2019 Stack Overflow Developer Survey Results Are InHelp on abstract algebra proof?Abstract Algebra (Ring Homomorphisms and Ideals)Abstract Algebra- IdealsAbstract Algebra .. HomomorphismAbstract Algebra 1 about permutationAbstract Algebra: Showing IsomorphismThe element that is an associate of everything.Show that this field is finite and count its elementsAbstract algebra: Associate elements of irreducible and prime elementsAssociate elements in non-integral domains.










-2












$begingroup$



In $Bbb Z[sqrt-7]$, show that $$N(6+2 sqrt-7)=N(1+3 sqrt-7)$$
but $6+2 sqrt-7$ and $1+3 sqrt-7$ are not associates




I don't know how to solve this. Help me to solve this!










share|cite|improve this question











$endgroup$



closed as off-topic by Arturo Magidin, Derek Holt, verret, YiFan, Shailesh Mar 25 at 0:24


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Arturo Magidin, Derek Holt, verret, YiFan, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.















  • $begingroup$
    means they differ by a unit, I believe
    $endgroup$
    – Sean Nemetz
    Mar 24 at 5:40










  • $begingroup$
    Please use MathJax instead of posting an image.
    $endgroup$
    – Toby Mak
    Mar 24 at 5:53






  • 1




    $begingroup$
    @Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
    $endgroup$
    – Michael Rozenberg
    Mar 24 at 6:21
















-2












$begingroup$



In $Bbb Z[sqrt-7]$, show that $$N(6+2 sqrt-7)=N(1+3 sqrt-7)$$
but $6+2 sqrt-7$ and $1+3 sqrt-7$ are not associates




I don't know how to solve this. Help me to solve this!










share|cite|improve this question











$endgroup$



closed as off-topic by Arturo Magidin, Derek Holt, verret, YiFan, Shailesh Mar 25 at 0:24


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Arturo Magidin, Derek Holt, verret, YiFan, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.















  • $begingroup$
    means they differ by a unit, I believe
    $endgroup$
    – Sean Nemetz
    Mar 24 at 5:40










  • $begingroup$
    Please use MathJax instead of posting an image.
    $endgroup$
    – Toby Mak
    Mar 24 at 5:53






  • 1




    $begingroup$
    @Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
    $endgroup$
    – Michael Rozenberg
    Mar 24 at 6:21














-2












-2








-2





$begingroup$



In $Bbb Z[sqrt-7]$, show that $$N(6+2 sqrt-7)=N(1+3 sqrt-7)$$
but $6+2 sqrt-7$ and $1+3 sqrt-7$ are not associates




I don't know how to solve this. Help me to solve this!










share|cite|improve this question











$endgroup$





In $Bbb Z[sqrt-7]$, show that $$N(6+2 sqrt-7)=N(1+3 sqrt-7)$$
but $6+2 sqrt-7$ and $1+3 sqrt-7$ are not associates




I don't know how to solve this. Help me to solve this!







abstract-algebra ring-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 24 at 6:04









Chinnapparaj R

6,34521029




6,34521029










asked Mar 24 at 5:37









Shivani ShahShivani Shah

6




6




closed as off-topic by Arturo Magidin, Derek Holt, verret, YiFan, Shailesh Mar 25 at 0:24


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Arturo Magidin, Derek Holt, verret, YiFan, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by Arturo Magidin, Derek Holt, verret, YiFan, Shailesh Mar 25 at 0:24


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Arturo Magidin, Derek Holt, verret, YiFan, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.











  • $begingroup$
    means they differ by a unit, I believe
    $endgroup$
    – Sean Nemetz
    Mar 24 at 5:40










  • $begingroup$
    Please use MathJax instead of posting an image.
    $endgroup$
    – Toby Mak
    Mar 24 at 5:53






  • 1




    $begingroup$
    @Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
    $endgroup$
    – Michael Rozenberg
    Mar 24 at 6:21

















  • $begingroup$
    means they differ by a unit, I believe
    $endgroup$
    – Sean Nemetz
    Mar 24 at 5:40










  • $begingroup$
    Please use MathJax instead of posting an image.
    $endgroup$
    – Toby Mak
    Mar 24 at 5:53






  • 1




    $begingroup$
    @Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
    $endgroup$
    – Michael Rozenberg
    Mar 24 at 6:21
















$begingroup$
means they differ by a unit, I believe
$endgroup$
– Sean Nemetz
Mar 24 at 5:40




$begingroup$
means they differ by a unit, I believe
$endgroup$
– Sean Nemetz
Mar 24 at 5:40












$begingroup$
Please use MathJax instead of posting an image.
$endgroup$
– Toby Mak
Mar 24 at 5:53




$begingroup$
Please use MathJax instead of posting an image.
$endgroup$
– Toby Mak
Mar 24 at 5:53




1




1




$begingroup$
@Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
$endgroup$
– Michael Rozenberg
Mar 24 at 6:21





$begingroup$
@Shivani Shah $N(a+bsqrtd)=a^2-db^2.$ Show us your trying.
$endgroup$
– Michael Rozenberg
Mar 24 at 6:21











1 Answer
1






active

oldest

votes


















1












$begingroup$

Hints:



  • $N(a+b sqrt-7)=vert a^2+7b^2 vert$

  • If both are associates, then $$6+2 sqrt-7=u cdot[ 1+3 sqrt-7]$$ where $u$ is a unit in $Bbb Z[sqrt-7]$. But the only possible units in $Bbb Z[sqrt-7]$ are........? and so......?





share|cite|improve this answer









$endgroup$



















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    Hints:



    • $N(a+b sqrt-7)=vert a^2+7b^2 vert$

    • If both are associates, then $$6+2 sqrt-7=u cdot[ 1+3 sqrt-7]$$ where $u$ is a unit in $Bbb Z[sqrt-7]$. But the only possible units in $Bbb Z[sqrt-7]$ are........? and so......?





    share|cite|improve this answer









    $endgroup$

















      1












      $begingroup$

      Hints:



      • $N(a+b sqrt-7)=vert a^2+7b^2 vert$

      • If both are associates, then $$6+2 sqrt-7=u cdot[ 1+3 sqrt-7]$$ where $u$ is a unit in $Bbb Z[sqrt-7]$. But the only possible units in $Bbb Z[sqrt-7]$ are........? and so......?





      share|cite|improve this answer









      $endgroup$















        1












        1








        1





        $begingroup$

        Hints:



        • $N(a+b sqrt-7)=vert a^2+7b^2 vert$

        • If both are associates, then $$6+2 sqrt-7=u cdot[ 1+3 sqrt-7]$$ where $u$ is a unit in $Bbb Z[sqrt-7]$. But the only possible units in $Bbb Z[sqrt-7]$ are........? and so......?





        share|cite|improve this answer









        $endgroup$



        Hints:



        • $N(a+b sqrt-7)=vert a^2+7b^2 vert$

        • If both are associates, then $$6+2 sqrt-7=u cdot[ 1+3 sqrt-7]$$ where $u$ is a unit in $Bbb Z[sqrt-7]$. But the only possible units in $Bbb Z[sqrt-7]$ are........? and so......?






        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Mar 24 at 6:23









        Chinnapparaj RChinnapparaj R

        6,34521029




        6,34521029













            Popular posts from this blog

            How should I support this large drywall patch? Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?How do I cover large gaps in drywall?How do I keep drywall around a patch from crumbling?Can I glue a second layer of drywall?How to patch long strip on drywall?Large drywall patch: how to avoid bulging seams?Drywall Mesh Patch vs. Bulge? To remove or not to remove?How to fix this drywall job?Prep drywall before backsplashWhat's the best way to fix this horrible drywall patch job?Drywall patching using 3M Patch Plus Primer

            random experiment with two different functions on unit interval Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Random variable and probability space notionsRandom Walk with EdgesFinding functions where the increase over a random interval is Poisson distributedNumber of days until dayCan an observed event in fact be of zero probability?Unit random processmodels of coins and uniform distributionHow to get the number of successes given $n$ trials , probability $P$ and a random variable $X$Absorbing Markov chain in a computer. Is “almost every” turned into always convergence in computer executions?Stopped random walk is not uniformly integrable

            Lowndes Grove History Architecture References Navigation menu32°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661132°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661178002500"National Register Information System"Historic houses of South Carolina"Lowndes Grove""+32° 48' 6.00", −79° 57' 58.00""Lowndes Grove, Charleston County (260 St. Margaret St., Charleston)""Lowndes Grove"The Charleston ExpositionIt Happened in South Carolina"Lowndes Grove (House), Saint Margaret Street & Sixth Avenue, Charleston, Charleston County, SC(Photographs)"Plantations of the Carolina Low Countrye