Rus Articles Journal

Fermat`s theorem for teapots?!! Be not afraid, it is not sick...

of 1. Why she is so famous?
You never know proved, unproven and not proved yet theorems? Here all the matter is that the Great theorem of Fermat is the biggest contrast between simplicity of the formulation and complexity of the proof.

the Great theorem of Fermat - the task incredibly difficult, and nevertheless its formulation can understand everyone with 5 - yu classes of high school, and here the proof - even not any mathematician - the professional. Neither in physics, nor in chemistry, nor in biology, nor in the same mathematics there is no problem which would be formulated so simply, but remained unresolved so long.

2. In what it consists? Let`s begin with Pythagorean trousers
the Formulation is really simple - at first sight. As it is known to us since the childhood, Pythagorean trousers on all parties are equal .

the Problem looks so simple because the mathematical statement which is known to all was the cornerstone of it, - Pythagorean theorem: the square constructed on a hypotenuse is equal in any rectangular triangle to the sum of the squares constructed on legs. That is it is easy to pick up a set of numbers which perfectly satisfy to equality x 2 + y 2 = z 2 . Since 3, 4, 5 - it is valid, it is clear to the junior school pupil that

9+16=25.

Or 5, 12, 13:

25 + 144 = 169.

Remarkably. Well and so on.

A if to take the similar equation x 3 + y 3 = z 3 ? Perhaps too there are such numbers? And so on (fig. 1).

And so, it turns out that they are absent.

Here the dirty trick begins. The simplicity - seeming because it is difficult to prove not existence something, and on the contrary, absence . When it is necessary to prove that the decision is, it is possible and it is necessary just to provide this decision. It is more difficult to prove absence: for example, somebody speaks: it is that equation has no decisions. To put him in a pool? easily: bang - and here it, the decision! (provide the decision). And everything, the opponent is struck. And how to prove absence? To tell: I did not find such solutions ? Or perhaps you badly looked for? And suddenly they are , only very big, well very much, such what even the heavy-duty computer does not have puny strength yet? This - that and is difficult.

In an evident look it can be shown so: if to take two small squares of the suitable sizes and to sort on single small squares, then from this small group of single small squares the third small square (fig. 2) turns out:

And we will do the same with the third measurement (fig. 3) - it is impossible. There are not enough cubes, or remain superfluous:

3. History: more than 350 years of search of decisions
the Theorem was formulated by Pierre Fermat in 1637 on fields of the book Arithmetics Diophantus with an addition that the witty proof of this theorem found him is too long that it could be placed here:

On the contrary, it is impossible to spread out a cube to two cubes, a biquadrate on two biquadrates and in general any degree, big a square, on two degrees with the same indicator. I found to it really wonderful proof, but fields of the book are too narrow for it.

A bit later Fermat published the proof of a special case for n = 4 that adds doubts that it had a proof of the general case, otherwise he by all means would mention it in this article. Euler in 1770 proved the theorem for n case = 3, Dirikhle and Legendre in 1825 - for n = 5, to Lama - for n = 7. Kummer showed that the theorem is right for all simple n, smaller 100 and so on. special cases, but not the universal proof for ALL NUMBERS were

But all this.

worked On a complete proof of the Great theorem many outstanding mathematicians, and these efforts led to receiving many results of the modern theory of numbers.

It is considered that the Great theorem is on the first place by the number of incorrect proofs. Many beginning mathematicians considered a duty to be risen to the Great theorem, but all was not possible to prove it in any way. At first hundred years did not work well. Then hundred more. Among mathematicians the mass syndrome began to develop: How so? Fermat proved, and I that, I will not be able perhaps? and some of them on this soil went mad in the true sense of the word.

Some tried to become famous for from the return: to prove that it is not faithful . And for this purpose, as we spoke, it is enough to give an example simply: there are three numbers, one cubed plus the second cubed - is equal to the third cubed. And they looked for such three of numbers. But unsuccessfully... And any computers with any speed, could never neither check the theorem nor disprove it, all variables of this equation (including exponents) can increase indefinitely.

4. At last!
At last on June 23, 1993 in Cambridge the most important lecture on mathematics in the XX century took place. , the Englishman, professor of Princeton university was a lecturer Andrew Uayls`s . Andrew Uayls showed to scientists a complete proof of the Great theorem of Fermat. It went to it 30 years, literally from ten-year age. Its proof was still specified and improved then in 1995, but the most important - the Great theorem was proved! On it the mankind needed 358 years . To the proof it was applied the highest and the most modern mathematical science. Therefore it is impossible to state this proof within a note in any way, and readers should take the word to me, mathematics of Cambridge and Princeton and so on.

Is the proof closed two pages of history at once: 350 - summer search of proofs of the Great theorem and infinite invasions of fermatist on all mathematical departments of all universities and institutes in the world.

5. Who such fermatist?
As it is told above, the formulation of the Great theorem is very simple and clear therefore there is a permanent illusion, as its proof also has to be simple , clear and be put in knowledge of algebra in volume of 5 - 6 classes. It generated incalculable crowds of the fanatics called by fermatist who tried to prove it thought that they proved, and attacked departments and certain scientists with the used-up notebooks in a section atilt. As all fanatics, they are intolerant of criticism, are full of intentions to demolish all barriers and are scary self-confident. Usually their thick works are thrown out at once, or given to students of department of the theory of numbers for search of a mistake as exercise.

As a rule, all proofs are consolidated to simple algebraic transformations: there added, here subtracted, squared everything, took a square root, curtailed on formulas of abridged multiplication, applied Newton binomial - and here it, proved. It is interesting that the most part of homebrew fermatist does not even understand a theorem essence - they prove not that the equation with exponents more than 2 has no whole decisions, and just try to prove that x in N degree + y in degree of N is equal to z in N degree that as you already, I hope, you understand, is deprived of all sense.

I prove! The mistake, as a rule, arises at the next construction of the equation in a square and the subsequent extraction of a root. It would seem - squared, then took a root - so on and will turn out, but they always forget that they x and (minus x) in a square are equal in a square. It is elementary, Watson!

Departments beat off as could. The scientific secretary of one of the Moscow academic institutes which did not avoid invasion of fermatist was on holiday in Moldova once and in the market bought some food which to it was wrapped in the local newspaper. Having returned from the market, he began to look through this leaf and came across a note in which it was reported that the local school teacher proved Fermat`s theorem, and, as a result, everyones were sung the praises of the high level of regional science. The scientific secretary cut out this note, and upon return to Moscow framed it and hung up on a wall of the office. Now, when on it attacked the next fermatist, he a broad gesture invited that to examine with current situation . Life became obviously easier. (Simon SINGH, VTF ).

I think, after everything that between us was, readers will be able already to estimate the telegram which got to me somehow at department in a lot of such manuscripts, notebooks and parcels post:

X of DEGREE of N PLUS Y of DEGREE of N PROVED FERMAT`S THEOREM of TChK ZET of DEGREE of N of TChK is EQUAL. The PROOF of DVTCh we TRANSFER Y of DEGREE of N the RIGHT PART of TChK of the DETAIL the LETTER