More to add to AP's 6th book//World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition by Archimedes Plutonium (Author).

A scientist, when he does a math proof or a physics theory, none of them leave you, none leaves you alone after a while. All of them continually nag you and the nagging never goes away. Such is the case of doing science. And sometimes in this nagging a new twist enters the picture. I have found this to be the case of nearly all my science work. Every time I write something on those discoveries, it is as if a new twist is bursting to come forth.

So on FLT which I proved in early 1990s, as early as 1991, my argument was that of a Basis Vector of Algebra is the reason no exponent 3 or higher has a solution. Of course, there are ample solutions in exponent 2 and more so in exponent 1.

But the new twist that dawned on me, is that a proof of FLT, should involve exp 1 and exp 2 and then exp3 and higher, as a mathematical induction proof.

Maybe we need not start at exp 1, for that is arithmetic A + B = C. Then exp 2 is the Pythagorean Theorem. So we have two starting true cases of the General FLT. For exp 2 we have the basis vector 2+2 = 2x2 =4, where we have a number that is equal under add and multiply. Now for exponent 1 we could say the basis vector is all of Arithmetic. Now for exponent 3, we cannot have no n+n+n = nxnxn = m, same for higher exponents.

So what I missed in my book was to emphatically suggest that a proof of FLT has to fully incorporate the exponents that do have solutions. Every mathematician before AP , looks at FLT in isolation of exponent 2, and by doing so, cut off their chances of finding a valid proof of FLT. Because the moment your mind asks the question, why no solutions in exp 3 but myriad solutions in exp 2, forces the mind to think that the valid proof has to incorporate in its proof mechanism, fully incorporate the picture that exp 2 has solutions not exp 3. And that then puts the onus of the mind to look at a Basis Vector where add is the very same as multiply.

Every Pythagorean theorem solution in Natural Counting Numbers has its basic building block of 2 and 4, of 2+2= 2x2= 4. Whereas every exp 3 is wanting a building block for all possible solutions, yet no numbers (except 0) have the ability to be k+k+k = kxkxk = m.

So I need to emphatically state in my 6th published book, that a proof of FLT, or even Generalized FLT should look at all exponents and not isolate exp2 from the higher exponents.

That is extremely important point of logic, that we tend to shove off to the side and want to focus all our attention on just a isolated problem, separate from the larger problem. We tend to separate, when we should look at the big picture to give us clues as to the mechanism of the proof.

So, actually, FLT was even absurdly more simple as a math problem and proof than most every other math proof in recorded history. FLT is more simple to prove than even the Pythagorean theorem is to prove. Because this is a proof of FLT. Proof: 2+2= 2x2= 4 allows us to build solutions in exp 2, but there does not exist a n+n+n = nxnxn = m so no solutions ever in exp 3 and the same argument for exp 4 and higher. QED

Totally simple proof is FLT, and if mathematicians had asked, what, ultimately what allows solutions in exp2 and said, well, well, 2+2=2x2 is the building block of all solutions in exp2.

No, my proofs in math and my theories in science and physics will never leave me alone, even if I tried. I can picture myself at my deathbed, and even there, one of my science theories will invade my mind as a die. Such, is the nature of a world of superdeterminism in an Atom Totality.

6th published book

World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 29Apr2021. This is AP's 6th published book.

Preface:
Real proofs of Fermat's Last Theorem// including the fake Euler proof in exp3 and Wiles fake proof.

Recap summary: In 1993 I proved Fermat's Last Theorem with a pure algebra proof, arguing that because of the special number 4 where 2 + 2 = 2^2 = 2*2 = 4 that this special feature of a unique number 4, allows for there to exist solutions to A^2 + B^2 = C^2. That the number 4 is a basis vector allowing more solutions to exist in exponent 2. But since there is no number with N+N+N = N*N*N that exists, there cannot be a solution in exp3 and the same argument for higher exponents. In 2014, I went and proved Generalized FLT by using "condensed rectangles". Once I had proven Generalized, then Regular FLT comes out of that proof as a simple corollary. So I had two proofs of Regular FLT, pure algebra and a corollary from Generalized FLT. Then recently in 2019, I sought to find a pure algebra proof of Generalized FLT, and I believe I accomplished that also by showing solutions to Generalized FLT also come from the special number 4 where 2 + 2 = 2^2 = 2*2 = 4. Amazing how so much math comes from the specialness of 4, where I argue that a Vector Space of multiplication provides the Generalized FLT of A^x + B^y = C^z.

Cover Picture: In my own handwriting, some Generalized Fermat's Last Theorem type of equations.

As for the Euler exponent 3 invalid proof and the Wiles invalid FLT, both are missing a proof of the case of all three A,B,C are evens (see in the text).
Length: 156 pages
File Size: 1503 KB
Print Length: 156 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PQKGW4M
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled 

More to add to AP's 6th book//World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition by Archimedes Plutonium (Author).

A scientist, when he does a math proof or a physics theory, none of them leave you, none leaves you alone after a while. All of them continually nag you and the nagging never goes away. Such is the case of doing science. And sometimes in this nagging a new twist enters the picture. I have found this to be the case of nearly all my science work. Every time I write something on those discoveries, it is as if a new twist is bursting to come forth.

So on FLT which I proved in early 1990s, as early as 1991, my argument was that of a Basis Vector of Algebra is the reason no exponent 3 or higher has a solution. Of course, there are ample solutions in exponent 2 and more so in exponent 1.

But the new twist that dawned on me, is that a proof of FLT, should involve exp 1 and exp 2 and then exp3 and higher, as a mathematical induction proof.

Maybe we need not start at exp 1, for that is arithmetic A + B = C. Then exp 2 is the Pythagorean Theorem. So we have two starting true cases of the General FLT. For exp 2 we have the basis vector 2+2 = 2x2 =4, where we have a number that is equal under add and multiply. Now for exponent 1 we could say the basis vector is all of Arithmetic. Now for exponent 3, we can have no n+n+n = nxnxn = m, same for higher exponents.

So what I missed in my book was to emphatically suggest that a proof of FLT has to fully incorporate the exponents that do have solutions. Every mathematician before AP , looks at FLT in isolation of exponent 2, and by doing so, cut off their chances of finding a valid proof of FLT. Because the moment your mind asks the question, why no solutions in exp 3 but myriad solutions in exp 2, forces the mind to think that the valid proof has to incorporate in its proof, a mechanism, a mechanism the spans and bridges between exponent 2 and exponent 3, fully incorporate the picture that exp 2 has solutions not exp 3. And that then puts the onus of the mind to look at a Basis Vector where add is the very same as multiply. So that solutions are metaphorically analogous to building concrete block buildings and the concrete blocks are the basis vector.

Every Pythagorean theorem solution in Natural Counting Numbers has its basic building block of 2 and 4, of 2+2= 2x2= 4. You can analyze every P-triple and find it is constructed of 2 and 4. Whereas every exp 3 is wanting a building block for all possible solutions, yet no numbers (not even 0 for the n and m have to be different) have the ability to be n+n+n = nxnxn = m.

So I need to emphatically state in my 6th published book, that a proof of FLT, or even Generalized FLT should look at all exponents and not isolate-out exp2 from the higher exponents.

That is extremely important point of logic, that we tend to shove off to the side and want to focus all our attention on just a part of the puzzle, a part of the problem, separate from the larger problem. We tend to separate, when we should look at the big picture to give us guidance and clues as to the mechanism of the proof.

So, actually, FLT was even absurdly more simple as a math problem and proof than most every other math proof in recorded history. FLT is more simple to prove than even the Pythagorean theorem is to prove. Because this is a proof of FLT. Proof: 2+2= 2x2= 4 allows us to build solutions in exp 2, but there does not exist a n+n+n = nxnxn = m so no solutions ever in exp 3 and the same argument for exp 4 and higher. QED

Totally simple proof is FLT, and if mathematicians had asked, what, ultimately what allows solutions in exp2 and said, well, well, 2+2=2x2 is the building block of all solutions in exp2.

No, my proofs in math and my theories in science and physics will never leave me alone, even if I tried. I can picture myself at my deathbed, and even there, one of my science theories will invade my mind as a die. Such, is the nature of a world of superdeterminism in an Atom Totality.

6th published book

World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 29Apr2021. This is AP's 6th published book.

Preface:
Real proofs of Fermat's Last Theorem// including the fake Euler proof in exp3 and Wiles fake proof.

Recap summary: In 1993 I proved Fermat's Last Theorem with a pure algebra proof, arguing that because of the special number 4 where 2 + 2 = 2^2 = 2*2 = 4 that this special feature of a unique number 4, allows for there to exist solutions to A^2 + B^2 = C^2. That the number 4 is a basis vector allowing more solutions to exist in exponent 2. But since there is no number with N+N+N = N*N*N that exists, there cannot be a solution in exp3 and the same argument for higher exponents. In 2014, I went and proved Generalized FLT by using "condensed rectangles". Once I had proven Generalized, then Regular FLT comes out of that proof as a simple corollary. So I had two proofs of Regular FLT, pure algebra and a corollary from Generalized FLT. Then recently in 2019, I sought to find a pure algebra proof of Generalized FLT, and I believe I accomplished that also by showing solutions to Generalized FLT also come from the special number 4 where 2 + 2 = 2^2 = 2*2 = 4. Amazing how so much math comes from the specialness of 4, where I argue that a Vector Space of multiplication provides the Generalized FLT of A^x + B^y = C^z.

Cover Picture: In my own handwriting, some Generalized Fermat's Last Theorem type of equations.

As for the Euler exponent 3 invalid proof and the Wiles invalid FLT, both are missing a proof of the case of all three A,B,C are evens (see in the text).
Length: 156 pages
File Size: 1503 KB
Print Length: 156 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PQKGW4M
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled 

🦇 of Math and 🦨 of Physics Archimedes "Drag Queen of Science"
Plutonium <plutonium.archimedes@gmail.com> fails at math and science:

> More to add to AP's 6th book//World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition by Archimedes Plutonium (Author).
>
The letters in "Archimedes Plutonium", rearranged, spell "Our Pandemic
Shit Mule".