Can Fermat's Last Theorem be proven for primes of the form 3k+1 and 3k+2?

  • Thread starter Thread starter smslca
  • Start date Start date
  • Tags Tags
    Theorem
AI Thread Summary
Fermat's Last Theorem asserts that there are no non-trivial integer solutions to the equation x^n + y^n = z^n for integers n greater than 2. The discussion highlights the relevance of prime numbers of the forms 3k+1 and 3k+2 in proving the theorem, noting that the proof for these primes differs significantly. It is suggested that proving the theorem for these specific primes could simplify the overall proof. The case for n=4 is mentioned as a classical example that is already established. The conversation emphasizes the complexity of the proof related to different prime forms.
smslca
Messages
63
Reaction score
0
fermat's last theorem?

What is Fermat's last theorem?
and How is that related to primes numbers of form 3x+1 and 3x+2
 
Mathematics news on Phys.org


FLT states: If n is an integer greater than 2, then there are no non-trivial integer solutions to the equation x^n+y^n=z^n.

One reduction for the proof is that it would be enough to prove the case when n is prime (or 4). The case n=4 is classical. It turns out that argument for primes of the form 3k+1 is different than for primes of the form 3k+2.

*warning, Latex seems out of whack today*
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Similar threads

Insights Fermat's Last Theorem
3
Replies
105
Views
6K
A Prime Number Powers of Integers and Fermat's Last Theorem
Replies
1
Views
2K
B Have I proved some part of Fermat's last theorem?
Replies
15
Views
2K
On Fermat’s last theorem and others....
Replies
13
Views
2K
B Fermat's Last Theorem; unacceptable proof, why?
Replies
12
Views
3K
I Proving Fermat's last theorem with easy math
Replies
2
Views
2K
I What is a good way to introduce Wilson's Theorem?
Replies
1
Views
1K
MHB Why isn't {0}^{3}+{0}^{3}={0}^{3} a proof for Fermat's Last Theorem?
Replies
3
Views
2K
MHB Find Last Two Digits of ${2017}^{82}$
Replies
12
Views
3K
The Current State of Mathematical Rigour
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top