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#1 2013-12-26 08:14:45
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
perfect square-proof
Hello!! 
I have a question.
If we know that j is a perfect square,how can we show that j+i*r is not always a perfect square for each i
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#2 2013-12-27 07:27:14
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
Hello!!
,where r is>0?
I have a question.
If we know that j is a perfect square,how can we show that j+i*r is not always a perfect square for each i
Can I prove it by contradiction? 
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#3 2013-12-27 08:48:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
I think you can easily disprove it by a counterexample.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2013-12-27 09:01:05
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
I think you can easily disprove it by a counterexample.
Do you mean that I have to take specific values for j and r?
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#5 2013-12-27 09:12:23
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
That would do it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2013-12-27 09:17:35
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
That would do it.
Nice,thank you and,is there also an other way,or is it the only one?
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#7 2013-12-27 09:23:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
Did you find a counterexample?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2013-12-27 09:30:33
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
Did you find a counterexample?
For
for ,so it is a perfect square
for ,that is not a perfect square
for ,that is not a perfect square.
Right?
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#9 2013-12-27 09:37:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
The great thing about doing numerical mathematics is you do not ever have ask the question, is it right. You did the calculation, you know it is right.
Yes, there are many counterexamples. The assertion is clearly false unless there are more conditions that you have omitted.
Why do you need anymore than that to convince anyone?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2013-12-27 09:54:22
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
The great thing about doing numerical mathematics is you do not ever have ask the question, is it right. You did the calculation, you know it is right.
Yes, there are many counterexamples. The assertion is clearly false unless there are more conditions that you have omitted.
Why do you need anymore than that to convince anyone?
I wanted to prove it by contradiction and tried this:
for
But I didn't know how to continue..
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#11 2013-12-27 10:12:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
Remember, it sometimes works! Trying to prove that it never does work is bound to fail.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2013-12-27 10:19:19
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
Remember, it sometimes works! Trying to prove that it never does work is bound to fail.
And can't I show that it is not always true?
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#13 2013-12-27 10:33:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
You did that with a counterexample. I am not seeing how to do it by contradiction yet.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2013-12-27 11:30:22
- evinda
- Member
- Registered: 2013-04-13
- Posts: 105
Re: perfect square-proof
You did that with a counterexample. I am not seeing how to do it by contradiction yet.
Ok...Thank you very much for your help!!!
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#15 2013-12-27 12:12:14
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
Using a counterexample here doesn't make sense.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#16 2013-12-27 15:08:59
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
It says show that it is not always a perfect square. That he has done?!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2013-12-27 21:28:29
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
He has shown with that that it is sometimes not a perfect square. Maybe it is still true for some other starting numbers.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#18 2013-12-27 21:58:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
He was asked to show that it is not always a perfect square. One example of each is good enough.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#19 2013-12-27 22:10:34
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
That is not correct. The statement is as follows:
That means we must prov it for all j and i, not prticular ones.
Last edited by anonimnystefy (2013-12-27 22:31:01)
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#20 2013-12-27 22:15:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
Prove what?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#21 2013-12-27 22:17:03
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
The statement I just posted.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#22 2013-12-27 22:20:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
Hi;
We did not prove it for all, we disproved it by counterexample. Isn't that what the question in post #1 asks for?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#23 2013-12-27 22:23:20
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
No, it is not. You have not read it.
Hi evinda
I found this link which does basically prove your statement, but does not look very simple.
Last edited by anonimnystefy (2013-12-27 22:23:50)
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#24 2013-12-27 22:28:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: perfect square-proof
I do not understand how that applies to his question in post #1.
In other words how can you prove that a false statement is true?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#25 2013-12-27 22:33:10
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: perfect square-proof
I am not doing that, because that statement is true.
In case you have not read the first post, which seems to be the case, it asks us to prove that, if j is a square number and r an integer, j+i*r is not always a square number.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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