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#1 2008-07-02 21:51:02

tony123
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Solve in positive integers the cubic

Solve in positive integers the cubic


x^3–(x+1)^2=2001

 

#2 2008-07-03 00:07:19

ZHero
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Re: Solve in positive integers the cubic

The solution (obviously) is 13 but you know how Dirty n Untidy n Ugly the cubic equations are to solve!!
If anyone's got a Good way to solve the above, please let me know!!cool


If two or more thoughts intersect with each other, then there has to be a point.
 

#3 2011-07-29 20:43:45

gAr
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Re: Solve in positive integers the cubic

Hi,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
 

#4 2011-08-03 17:34:04

bobbym
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Re: Solve in positive integers the cubic

Hi;

He probably graphed the equation and eyeballed the root as 13. This is an acceptable conjecture which can be proved by plugging in. A little fortuitious but... Then it is trival to prove that it is the only positive root.

You would deflate out the obvious root.



The discriminant of the right side is - 472, so 13 is the only positive root.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#5 2012-05-03 09:35:35

anonimnystefy
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Re: Solve in positive integers the cubic

Another way is to use the method developed for solving a general cubic. It is given in a thread of mine and is available on the net.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

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