Solution needed 4 a very good problem

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Discussion Overview

The discussion revolves around finding integer solutions to the equation x^3 - y^2 = 2006. Participants explore various mathematical approaches and share their experiences with the problem, which appears to be rooted in number theory.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant asks what methods others have tried and what mathematics they are familiar with regarding the problem.
  • Another participant suggests it may be a number theory problem and questions if anyone knows a solution.
  • A participant claims to have a solution derived from using Mathematica but expresses a desire to understand the mathematical background of others to provide better assistance.
  • One participant attempts to manipulate the equation by substituting y in terms of x but questions their approach and expresses uncertainty about how to proceed.
  • Another participant critiques the substitution method, stating it leads to a trivial identity rather than a solution.
  • A participant mentions solving the equation through guess and check, despite not knowing the underlying theory.
  • There is a question raised about whether this problem is related to math olympiad challenges.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution or the methods to approach the problem. Multiple viewpoints and methods are presented, indicating ongoing exploration and uncertainty.

Contextual Notes

Some participants express limitations in their mathematical knowledge, and there are unresolved steps in the reasoning presented. The discussion reflects varying levels of familiarity with number theory and problem-solving techniques.

Who May Find This Useful

This discussion may be of interest to those studying number theory, participants in math competitions, or individuals looking for collaborative problem-solving approaches in mathematics.

rahul963
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Solve x^3 - y^2 = 2006 in integers.
 
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What have you tried so far? What sort of mathematics have you learned to solve this problem?
 
number theory problem? do u knowsolution r not?
 
zurtex? do u hve ny idea?
 
rahul963 said:
zurtex? do u hve ny idea?
Well yes I do know a solution and I would have a guess it's the only solution, but I only know this solution by running the problem through mathematica, I was wondering what sort of number theory you know so I might be able to help you rather than just give you an answer.
 
[tex]x^3 - y^2 = 2006[/tex]

[tex]y^2 = x^3 - 2006[/tex]

[tex]y = \sqrt{x^3 - 2006}[/tex]

So then, using substitution...

[tex]x^3 - \sqrt{x^3 - 2006} = 2006[/tex]

I'm sure this isn't nearly sophisticated enough, and I've probably gotten into a rut of some sort (I know I don't know how to continue ><)... It's what I tried, though-- and now I'm curious as to how you would continue, or if I'm completely wrong... If this is digressing from the topic, I apologize-- just ignore me if that is the case...
 
Last edited:
You can't do that. You have a single equation with two variables which you substituted back into your equation. It will give you something in along the lines of 0 = 0 or x = x. And it does:

[tex]x^3 - x^3 + 2006 = 2006[/tex]
 
I don't know the theory behind it, but it only took a few minutes of guess and check to solve.
 
rahul963 said:
Solve x^3 - y^2 = 2006 in integers.

Is this a math olympiad problem by any chance?
 

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