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

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In summary, the conversation revolves around finding a natural number n greater than 2 where the equation a^n + b^n = c^n is satisfied using real numbers a, b, and c. One suggestion is to take n = 3 and a = 1, b = 2, and c = 3^(2/3). However, it is noted that for integers a, b, and c, there are no solutions due to Fermat's Last Theorem. The conversation also touches on the difference between real numbers and integers, and clarifies that the poster was referring to real numbers.
  • #1
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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  • #2
Sure, no problem. Take n = 3 and a = 1, b = 2 and c = 3^(2/3)...
 
  • #3
http://en.wikipedia.org/wiki/Fermat's_last_theorem

There are none for integers a,b, and c.
 
  • #4
yep it is fermat's theorem...ok thank you!
 
  • #5
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.
 
  • #6
He just neglected to mention the integer requirement, which I amended.
 
  • #7
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".
 
  • #8
How is that not neglecting to mention the integer requirement.
 
  • #9
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.
 

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

What is the meaning of "Solving "A Little Problem" with a^n+b^n=c^n"?

"Solving "A Little Problem" with a^n+b^n=c^n" refers to finding the values of a, b, and c that satisfy the equation a^n + b^n = c^n, where n is a positive integer greater than 2. This problem is also known as Fermat's Last Theorem, and it was famously proved by mathematician Andrew Wiles in 1994.

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Solving this problem has been a longstanding challenge in the field of mathematics. It was first proposed by French mathematician Pierre de Fermat in the 17th century and has since been attempted by countless mathematicians. The solution to this problem has significant implications for number theory and has also led to advancements in other areas of mathematics.

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There are many other unsolved problems in mathematics that are related to Fermat's Last Theorem. Some of these include the Beal Conjecture, which deals with solutions to equations of the form a^x + b^y = c^z, and the ABC Conjecture, which is a generalization of Fermat's Last Theorem. Other related problems include the Collatz Conjecture and the Goldbach Conjecture.

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