The Uzbek mathematician B.Ponomarev solved Fermat's theorem! Check?
Long ago, in 1637, Pierre Fermat had the folly of writing the following on Diofant's “Arithmetic” fields: “... it is impossible to decompose a cube into two cubes, a biquadrate into two biquadrats, and no degree at all, a large square, two degrees with the same indicator. I found this truly miraculous proof, but the margins of the book are too narrow for him. ”
After this, the statement that no degree, greater than a square, cannot be decomposed into two degrees with the same index is called the Great Fermat theorem. The simple formulation has provided her with great popularity among professional mathematics and amateur scientists.
Despite this, it was fully proven only in 1995, using theories of elliptic curves.
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Recently, several quite authoritative by local standards news portals were blown up by the news: Uzbek mathematician solved Fermat's theorem - Mathematician from Tashkent Boris Ponomarev claims that he found “simple original proof” of Great Fermat's theorem - riddles that scientists of the whole world have been fighting for 350 years now ( for example, here , here and here ). In one of them was even given evidence .
I immediately became interested tolook for a mistake to look at the solution. It will be a great honor for all of us if a representative of the Soviet school of education has found evidence that is being searched all over the world for more than 350 years.
Let's go back to the solution itself: It consists of only 7 scanned jpeg sheets. The first page is the title with the photo of the author of the decision. I saw a typical mathematician (I am the same). At the very top, proudly written off — I dedicate to the great Russian mathematicians — past, present, and future.
The second page is the Introduction. Here is written the extended history of the theorem, and many more words about “mathematical truth”. The last sentence, "I ... piously follow this covenant," is more like an oath (more and more you hope that this is the right decision of the theorem that everyone was looking for and seeing that they will admire), and Orion NZ's signature (the author's nickname?).
In the third page , the solution itself begins, and it begins with three obvious and not very statement (lemmas). I was embarrassed by the expression (and not only that - the terminology with time, unfortunately, is becoming more and more different) “the whole base of the equation” in the first lemma, but I understood it as for every integer value x there will be at least 2 integer pairs (y, z) satisfying the equation, then the first lemma will be true, even quite obvious. In the second lemma, I did not understand why they considered it trivial to not take the cube root from the expression, in my opinion this is no less obvious than Fermat's theorem for the case n = 3. Despite this, I do not doubt the truth of the author’s statement.
But the most important puncture is on the fourth page , with the proof of Lemma number 3. In the sentence in the second paragraph “... the product (n) of the basis (x) allows only one matrix in the field of integers (again problems with terminology?) Into two values x ^ k and x ^ (nk) are exactly equal to the factors (zy) and (z + y) ”obviously an incorrect statement. A counterexample, any uneasy x, for example x = 6, and n = 3, z = 55, y = 53. A puncture, and it is not the only, most absurd, which makes all further arguments meaningless.
At the first look at the fifth and sixth pages, before finding the previous punctures, I was delighted: I used to think that if Fermat proved the theorem, he also divided the equation into z ^ n and worked with fractions. In the seventh last page, trivial reasoning on the topic of changing signs. It’s a pity, as we wouldn’t be sad to admit it, but this “solution” is wrong (with sadness).
It is said that Fermat himself later published a special case for n = 4, which makes it doubtful that he had proof of the general case, using knowledge known in the 17th century. I wonder if it is there at all?
UPD : Barmaleikin user added a link to the Soviet 20-minute feature film about the Great Farm Theorem in the comments, pulling it here. I advise lovers of mathematics to watch this movie is a pleasure.
Link to youtube .
After this, the statement that no degree, greater than a square, cannot be decomposed into two degrees with the same index is called the Great Fermat theorem. The simple formulation has provided her with great popularity among professional mathematics and amateur scientists.
Despite this, it was fully proven only in 1995, using theories of elliptic curves.
')
Recently, several quite authoritative by local standards news portals were blown up by the news: Uzbek mathematician solved Fermat's theorem - Mathematician from Tashkent Boris Ponomarev claims that he found “simple original proof” of Great Fermat's theorem - riddles that scientists of the whole world have been fighting for 350 years now ( for example, here , here and here ). In one of them was even given evidence .
I immediately became interested to
Let's go back to the solution itself: It consists of only 7 scanned jpeg sheets. The first page is the title with the photo of the author of the decision. I saw a typical mathematician (I am the same). At the very top, proudly written off — I dedicate to the great Russian mathematicians — past, present, and future.
The second page is the Introduction. Here is written the extended history of the theorem, and many more words about “mathematical truth”. The last sentence, "I ... piously follow this covenant," is more like an oath (more and more you hope that this is the right decision of the theorem that everyone was looking for and seeing that they will admire), and Orion NZ's signature (the author's nickname?).
In the third page , the solution itself begins, and it begins with three obvious and not very statement (lemmas). I was embarrassed by the expression (and not only that - the terminology with time, unfortunately, is becoming more and more different) “the whole base of the equation” in the first lemma, but I understood it as for every integer value x there will be at least 2 integer pairs (y, z) satisfying the equation, then the first lemma will be true, even quite obvious. In the second lemma, I did not understand why they considered it trivial to not take the cube root from the expression, in my opinion this is no less obvious than Fermat's theorem for the case n = 3. Despite this, I do not doubt the truth of the author’s statement.
But the most important puncture is on the fourth page , with the proof of Lemma number 3. In the sentence in the second paragraph “... the product (n) of the basis (x) allows only one matrix in the field of integers (again problems with terminology?) Into two values x ^ k and x ^ (nk) are exactly equal to the factors (zy) and (z + y) ”obviously an incorrect statement. A counterexample, any uneasy x, for example x = 6, and n = 3, z = 55, y = 53. A puncture, and it is not the only, most absurd, which makes all further arguments meaningless.
At the first look at the fifth and sixth pages, before finding the previous punctures, I was delighted: I used to think that if Fermat proved the theorem, he also divided the equation into z ^ n and worked with fractions. In the seventh last page, trivial reasoning on the topic of changing signs. It’s a pity, as we wouldn’t be sad to admit it, but this “solution” is wrong (with sadness).
It is said that Fermat himself later published a special case for n = 4, which makes it doubtful that he had proof of the general case, using knowledge known in the 17th century. I wonder if it is there at all?
UPD : Barmaleikin user added a link to the Soviet 20-minute feature film about the Great Farm Theorem in the comments, pulling it here. I advise lovers of mathematics to watch this movie is a pleasure.
Link to youtube .
Source: https://habr.com/ru/post/137749/
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