If $P^2$ is an integer, is $P$ also an integer?
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Suppose that $P^2 in Bbb Z$ where $Bbb Z$ is the set of all integers. Can you conclude $P in Bbb Z$?
elementary-number-theory discrete-mathematics
edited Dec 1 at 18:49
Jam
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
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up vote
-3
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Suppose that $P^2 in Bbb Z$ where $Bbb Z$ is the set of all integers. Can you conclude $P in Bbb Z$?
elementary-number-theory discrete-mathematics
edited Dec 1 at 18:49
Jam
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
2
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52
|
show 1 more comment
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Suppose that $P^2 in Bbb Z$ where $Bbb Z$ is the set of all integers. Can you conclude $P in Bbb Z$?
elementary-number-theory discrete-mathematics
edited Dec 1 at 18:49
Jam
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
Suppose that $P^2 in Bbb Z$ where $Bbb Z$ is the set of all integers. Can you conclude $P in Bbb Z$?
elementary-number-theory discrete-mathematics
elementary-number-theory discrete-mathematics
edited Dec 1 at 18:49
Jam
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
edited Dec 1 at 18:49
Jam
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
edited Dec 1 at 18:49
Jam
4,87011431
edited Dec 1 at 18:49
Jam
4,87011431
edited Dec 1 at 18:49
Jam
4,87011431
4,87011431
asked Nov 27 at 7:39
Maryam Hak
13
asked Nov 27 at 7:39
Maryam Hak
13
asked Nov 27 at 7:39
Maryam Hak
13
13
No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
2
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52
|
show 1 more comment
No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
2
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52
No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
2
2
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52
|
show 1 more comment
1 Answer
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Surely not. Take $p=sqrt 2approx 1.4142$ where $pnotinBbb Z$ while $p^2=2inBbb Z$
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
add a comment |
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1 Answer
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up vote
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Surely not. Take $p=sqrt 2approx 1.4142$ where $pnotinBbb Z$ while $p^2=2inBbb Z$
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
add a comment |
up vote
1
down vote
Surely not. Take $p=sqrt 2approx 1.4142$ where $pnotinBbb Z$ while $p^2=2inBbb Z$
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
add a comment |
up vote
1
down vote
up vote
1
down vote
Surely not. Take $p=sqrt 2approx 1.4142$ where $pnotinBbb Z$ while $p^2=2inBbb Z$
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
Surely not. Take $p=sqrt 2approx 1.4142$ where $pnotinBbb Z$ while $p^2=2inBbb Z$
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
answered Nov 27 at 8:03
Mostafa Ayaz
13.6k3836
13.6k3836
add a comment |
add a comment |
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No. There are many counterexamples.
– Sean Roberson
Nov 27 at 7:43
$(sqrt 2)^2in Bbb Z$
– 1ENİGMA1
Nov 27 at 7:44
2
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 27 at 7:50
Hi, @JoséCarlosSantos. Is it okay if I copy your comment to use on other questions like this? It's a very good summary of how not to ask a question.
– Jam
Dec 1 at 18:44
@Jam Of course. And please don't think that I created it. I took it from here.
– José Carlos Santos
Dec 1 at 18:52