Beal's conjecture prize

Originally Posted by MattcAnderson

Hi again everybody,

One of them was (sort of) recently solved.
Now, let's look at the Beal conjecture. It is a generalization of
Fermat's last theorem.

The Beal Conjecture is something like
a^x + b^y = c^z
where all variables are both positive and integers.

This is the sort of problem that definitely takes collaboration. One person cannot (yet) do it alone.
IMHO (In My Humble Opinion)

Matt, one of my tenets in reading through this forum is to recognize the source where conclusions can be drawn from that alone. Your post brought up (double entendre here) some points which you could address..such as the following:
Mathematical precision in statement, description and resolution must be considered. Wishy-washiness, inaccurate paraphrasing and bold hyperbole (closely affiliated with unfounded conjectures) should be avoided if you're aware of them.
I've been guilty of all of the above and have adapted (most of) my posts accordingly within this forum..one example of mine was mis-stating attributes of the critical line and I was brought to task on this. Chronic repetition of mistakes be they thematic or expository is not a desirable trend to maintain.

Regarding the first two points mentioned above, do your homework and learn more about both. If you read about the resolution of the Poincare Conjecture you will learn something about human nature which goes to your third point. Try to understand, to the best of your ability, this conjecture and its solution. Next, read about the "attribution" of the solution and what took place..and where the money eventually went.
Since I also like to play poker, (Yardley did as well..an interesting bloke), read "The Professor, the Banker, and the Suicide King." This conjecture is deep and I don't understand it as well as the one above. I have followed up with purported proofs which had some interesting approaches and have cross referenced them with reviewers to learn more. A good exercise to test your technical sagacity is to "spot the mistake in the proof" ...or any disqualified proof to address your mathematical chops..without peeking of course.

To your third point, read up on https://en.wikipedia.org/wiki/Grigori_Perelman rather than just being "barely familiar" with who he is. Conceptual advances made by committees are vastly overshadowed by those made by indivuals. I read the following novella years ago when it first came out and I recommend this updated version to you now..https://www.amazon.ca/SYSTEMANTICS-S.../dp/B00AK1BIDM

Regarding some of the other posts within this thread and references to pythagorean triangles, does anyone have a pointer to a comprehensive listing of congruent numbers (other than primes 5,6,7 mod 8)? Sardonicus?..anyone ..anyone?*

*If anyone watched "Win Ben Stein's Money" they'll get the reference. By the way, the show was hosted by Jimmy Kimmel and Ben Stein was an advisor to Nixon..both smart and funny men.
https://www.youtube.com/watch?v=zROOIwTlfgE


For the sake of completion, here's a link to Yardley's poker book, https://www.amazon.ca/Education-Poke.../dp/487187639X. He has written more books which are also "educational." However, due diligence is always required..https://ia600903.us.archive.org/21/i..._watermark.pdf.
A slight tangent will take you to this Canadian..https://en.wikipedia.org/wiki/William_Stephenson..a small plug for Canucks.

[xilman]

Originally Posted by jwaltos

Regarding some of the other posts within this thread and references to pythagorean triangles, does anyone have a pointer to a comprehensive listing of congruent numbers (other than primes 5,6,7 mod 8)? Sardonicus?..anyone ..anyone?*

*If anyone watched "Win Ben Stein's Money" they'll get the reference. By the way, the show was hosted by Jimmy Kimmel and Ben Stein was an advisor to Nixon..both smart and funny men.
https://www.youtube.com/watch?v=zROOIwTlfgE


For the sake of completion, here's a link to Yardley's poker book, https://www.amazon.ca/Education-Poke.../dp/487187639X. He has written more books which are also "educational." However, due diligence is always required..https://ia600903.us.archive.org/21/i..._watermark.pdf.
A slight tangent will take you to this Canadian..https://en.wikipedia.org/wiki/William_Stephenson..a small plug for Canucks.

That is one thing I really like about this place - I often learn something new and unexpected.

I had never heard of "Yardley's poker book" but own a 1st-edition copy of The American Black Chamber. I wondered if it was the same Yardley and followed your second link. Sure enough, it is. It would have been obvious if the full text of your third link had been visible but the forum had chopped out the interesting central portion.

[storm5510]

I did some coding experiments and came up with these, among many others:

(52572 ^ 21150) + (503141 ^ 24504) - (586043 ^ 196) <> 0
(411808 ^ 24036) + (673730 ^ 12731) - (321725 ^ 7257) <> 0
(18836 ^ 5853) + (3706 ^ 19816) - (30804 ^ 32334) <> 0

I read the pertinent part of this first. An excerpt:

a^x + b^y = c^z

a, b, c, x, y, and z are positive integers with (x, y, and z) > 2.
a, b, and c have a common prime factor.

Following kriesel's suggestion, I calculated for zero. I kept a scant few results to see how large they were. One was over 176,000 digits in length.

The OP wrote one person cannot do this alone, yet. As it is now, a great many, and their descendants, could run this for decades and never find a zero result. For me, it was simply a learning experience.