Matematici spiegateci tutto !
I advise those who is not so alien mathematicians, to check up Ilyin's calculations alone with a paper leaf. Probably, it will demand from you some pressure, but it will be voznagrazhdeno, probably, you become witnesses of a birth of a miracle.
So, it is required to prove, that if X and Y - integers in equation X n + Y n = Z n, Z, at n it is more 2, - always not the whole. Before to undertake for the Farm, we shall repeat theorem Pifagora: " the Square of a hypotenuse is equal to the sum of squares of cathetuses ". We have the right to use any variables for its writing. We shall write down it thus: X 2 + Y 2 = R 2, where X, Y, R - integers, and Z, the Farm, - not approves the whole. We shall try to prove. Clearly, Z it is not equal R at the same X, Y. Legkodokazuemo algebraically, and simply logically, that Z always it is less, than R. When we erect X and Y in higher degree we multiply them by themselves. Then them we put and we receive Z in the same degree n. And at erection in it R each of composed should be increased on R which is more, than X and Y.
For example, R 3 = (X 2 + Y 2) R = X 2 R+Y 2 R.
What does Ilyin do? Anything especial. Writes down lengths of the parties of triangle XYR in a trigonometrical kind: X = R sin A, Y = R cos A. So, Z n = X n + Y n = R n (sin A + cos A). What is the root, you have not forgotten?
Perfectly. Z = R ?sin A + cos A. Earlier we have proved, that Z always it is less R, so, sin A + cos A <1. Such trigonometrical function can be found in any textbook of mathematics of the senior classes and to be convinced under the schedule or the table, that if value of function <1 corner A is more than 60 and less 90 degrees. And what will occur in this case to a right angle In, being between cathetuses? It more any more will not be to straight lines and it will appear in the same limits: 60 o <B <90 o. Not without reason in fact " ninety, sixty, " it is considered ninety an ideal of harmony. It is a silly joke that you have a little relaxed. Because we are already close to finish. Any ninth-grader at whom on the mathematician above a three, straight off will reproduce to you the formula of a parity of the parties of triangle Z 2 = X 2 + Y 2 - 2 XY cos B. We shall consider expression. At 60 o <B <90 o cos B - number not the whole. So, and Z inevitably is those at whole values X and Y. As was to be shown.
http://www.online-translator.com/url...n61n-s00.shtml