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#1 2008-07-01 23:51:02

tony123
Member
Registered: 2007-08-03
Posts: 189

Solve in positive integers the cubic

Solve in positive integers the cubic


x^3–(x+1)^2=2001

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#2 2008-07-02 02:07:19

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

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, there has to be a point!

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#3 2011-07-28 22:43:45

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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."

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#4 2011-08-02 19:34:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,351

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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#5 2012-05-02 11:35:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

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.


“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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