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https://www.techrxiv.org/users/717330/articles/702287-on-fermat-s-last-theorem https://www.techrxiv.org/users/717330/articles/702287-on-fer...

by levn11 2y ago

voldacar 2y ago
Why post this? This appears to be the writings of a crank.
- levn11 2y ago
  which part
  - n4r9 2y ago
    On p.4 you argue that for integers a, b, c and n: (a + b − c)^n = (c − a)(c − b)g_1(n) => a + b − c = [(c − a)(c − b)g_1(n)]^(1/n) => g_1(n) | a + b - c This doesn't follow as it stands. For example, if a=b=3 and c=n=2, then g_1(n)=16 whereas a + b - c = 4.
  - voldacar 2y ago
    The part in which FLT is derived from the binomial theorem, lol.
    - hughesjj 2y ago
      Nah not derived, set equal to from the outset with essentially no explanatory test throughout but with enough effort to insert some arbitrary graphs and label them with 'hey neato look at the vibes'
      - voldacar 2y ago
        My favorite part is "The derivative resembles the rhythm of a heartbeat."
n4r9 2y ago
This would definitely benefit from a bit more explanatory text as I'm struggling to understand what you've shown. The crux seems to be that if a^n+b^n=c^n then (c-a)(c-b) divides (a+b-c)^n. I haven't been through all the details of this, but I also don't see how that implies FLT.
- hughesjj 2y ago
  If I'm not mistaken Fermat's last theroem isn't even featured in the proof. Like nowhere did I see a^n+b^n=c^n referenced in the proof,save for the end of page 1 and 3, but it's never featured in an equality. Just 'this implies this trust me bro'.
  - n4r9 2y ago
    I've actually had another quick look and I now have a vague idea of the outline. It's an attempted proof by contradiction, where a solution to FLT is applied to the binomial theorem and some arguments about integrality are made to form a contradiction. My issue at the moment is with a line at the bottom of p.4, which effectively says that if k^n = xy for integers k, n, x, y, then k must be a multiple of y. Unless I'm missing something this is clearly false, for example 2^4 = 4 x 4.

https://www.techrxiv.org/users/717330/articles/702287-on-fermat-s-last-theorem https://www.techrxiv.org/users/717330/articles/702287-on-fer...

by levn11 2y ago

https://www.techrxiv.org/users/717330/articles/702287-on-fermat-s-last-theorem https://www.techrxiv.org/users/717330/articles/702287-on-fer...

voldacar 2y ago

Why post this? This appears to be the writings of a crank.

levn11 2y ago
which part
- n4r9 2y ago
  On p.4 you argue that for integers a, b, c and n: (a + b − c)^n = (c − a)(c − b)g_1(n) => a + b − c = [(c − a)(c − b)g_1(n)]^(1/n) => g_1(n) | a + b - c This doesn't follow as it stands. For example, if a=b=3 and c=n=2, then g_1(n)=16 whereas a + b - c = 4.
- voldacar 2y ago
  The part in which FLT is derived from the binomial theorem, lol.
  - hughesjj 2y ago
    Nah not derived, set equal to from the outset with essentially no explanatory test throughout but with enough effort to insert some arbitrary graphs and label them with 'hey neato look at the vibes'
    - voldacar 2y ago
      My favorite part is "The derivative resembles the rhythm of a heartbeat."

n4r9 2y ago

This would definitely benefit from a bit more explanatory text as I'm struggling to understand what you've shown. The crux seems to be that if a^n+b^n=c^n then (c-a)(c-b) divides (a+b-c)^n. I haven't been through all the details of this, but I also don't see how that implies FLT.

hughesjj 2y ago
If I'm not mistaken Fermat's last theroem isn't even featured in the proof. Like nowhere did I see a^n+b^n=c^n referenced in the proof,save for the end of page 1 and 3, but it's never featured in an equality. Just 'this implies this trust me bro'.
- n4r9 2y ago
  I've actually had another quick look and I now have a vague idea of the outline. It's an attempted proof by contradiction, where a solution to FLT is applied to the binomial theorem and some arguments about integrality are made to form a contradiction. My issue at the moment is with a line at the bottom of p.4, which effectively says that if k^n = xy for integers k, n, x, y, then k must be a multiple of y. Unless I'm missing something this is clearly false, for example 2^4 = 4 x 4.