Solving "A Little Problem" with a^n+b^n=c^n

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Discussion Overview

The discussion revolves around the problem of finding natural numbers n greater than 2 such that the equation a^n + b^n = c^n holds for real numbers a, b, and c. The scope includes theoretical exploration and references to established mathematical theorems.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant presents the problem and expresses uncertainty about their proposed solution.
  • Another participant suggests specific values for a, b, and c, claiming they satisfy the equation for n = 3.
  • A reference to Fermat's Last Theorem is made, indicating that no solutions exist for integers a, b, and c.
  • Some participants argue that for real numbers a, b, and c, there are infinitely many solutions for any natural number n.
  • There is a contention regarding whether the original poster neglected to specify the integer requirement, with differing interpretations of the problem's wording.
  • Participants discuss the implications of the distinction between real numbers and integers in the context of the problem.

Areas of Agreement / Disagreement

Participants disagree on the interpretation of the problem regarding the requirement for integers versus real numbers, leading to differing views on the existence of solutions. The discussion remains unresolved regarding the implications of these distinctions.

Contextual Notes

The discussion highlights the ambiguity in the problem's wording and the differing mathematical contexts (real numbers vs. integers) that affect the interpretation of potential solutions.

tyutyu fait le train
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Here is the question: "could you fine n>2 (n natural number) so that: a^n+ b^n=c^n with a, b and c real numbers".

I have got an idea but I am not sure if it works.

Thank you very much

tyu
 
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Sure, no problem. Take n = 3 and a = 1, b = 2 and c = 3^(2/3)...
 
http://en.wikipedia.org/wiki/Fermat's_last_theorem

There are none for integers a,b, and c.
 
yep it is fermat's theorem...ok thank you!
 
But what you posted isn't Fermat's Last Theorem. For real a,b and c, there are an infinite number of solutions for every natural number value of n.
 
He just neglected to mention the integer requirement, which I amended.
 
whozum said:
He just neglected to mention the integer requirement, which I amended.

No he didn't neglect anything, he said "with a, b and c real numbers".
 
How is that not neglecting to mention the integer requirement.
 
whozum said:
How is that not neglecting to mention the integer requirement.
The Real Number set is an entirely different number set to the Integers. The poster said Real Numbers.
 
  • #10
The issue here is of word choice. I said "neglecting to mention the integer requirement" is the same as "not mentioning the integer requirement".

He mentioned a problem very similar to FLT in which I referenced him to the correct form. It turns out that is what he is looking for.
 

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