What is a Possible Algebraic Proof of Case 1 of Fermat's Last Theorem?

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In summary, the conversation discusses various "proofs" of Fermat's Last Theorem (FLT) and the difficulty in finding a proof that is easily understandable by those without a strong background in higher mathematics. The link provided presents a possible algebraic proof for Case 1, but there are questions about the conditions and factors involved. The conversation concludes with the understanding that the stronger position is being assumed and the factor h cannot have any n factors.
  • #1
vantheman
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Most with any knowledge of Number Theory are aware that many hundreds of thousands of hours have been spent reviewing flawed "proofs" of Fermat's Last Theorem (FLT). It is understandable that a serious mathematician would not spend more than a few minutes looking at a possible "proof". Wiles' proof is magnificient, if you have a strong background in higher mathematics, which very few do. The link below is a 'possible' algebraic proof of Case 1 that, if it doesn't have a fatal flaw, may be a solution that a math undergraduate can understand. I hope you will not find it a waste of time to take a look.

http://dutch-fltcase1.blogspot.com/
 
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  • #2
Hi, vantheman,
I have a couple of questions:

1) Case 1 says "n divides neither of x,y,z"; yet for Section I, at the beginning of page 9, you take the condition (n,x) = (n,y) = (n,z) = 1, which is much stronger. (For example, 6 does not divide any of 8, 11, 17, yet it has a common factor with the first of them.)

2) Also on page 9, eq.1.6, I believe you are trying to find a factor h in the right-hand side, and all terms have one h except the last, a^n . n^(n-2). Why can't the factor h be in n^(n-2)? Or, for that matter, h could be composite, with some of its prime factors in a^n and the others in n^(n-2).

Thanks
 
  • #3
I am assuming the stronger position - n does not divide x, y or z and x, y and z have no common factors.

Since n does not divide y , n does not divide h, since y == h mod n. Therefore h cannot have any n factors.
 

1. What is Fermat's Last Theorem Case 1?

Fermat's Last Theorem Case 1 is a mathematical conjecture proposed by Pierre de Fermat in the 17th century. It states that for any three positive integers a, b, and c, the equation a^n + b^n = c^n has no positive integer solutions when n is greater than 2.

2. Why is Case 1 of Fermat's Last Theorem considered the most difficult?

Case 1 of Fermat's Last Theorem is considered the most difficult because it requires proving the non-existence of solutions for an infinite number of cases. In contrast, the other cases of the theorem have finite solutions or can be disproved using counterexamples.

3. Who proved Case 1 of Fermat's Last Theorem?

Case 1 of Fermat's Last Theorem was finally proved by British mathematician Andrew Wiles in 1994, after more than 350 years of attempted proofs by various mathematicians.

4. What is the significance of Fermat's Last Theorem?

Fermat's Last Theorem is considered one of the most famous and important problems in mathematics. Its solution has implications in number theory, algebra, and geometry, and has opened up new avenues of research in these fields.

5. Are there any practical applications of Fermat's Last Theorem?

While there are no direct practical applications of Fermat's Last Theorem, the techniques used to prove it have been applied in other areas of mathematics and have led to the development of new mathematical tools and concepts.

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