ONE APPROACH TO THE PROOF OF THE GRAND THEOREM OF THE FERMAT’S FOR THE EXPONENT 4
The «Great theorem of Fermat», which was born by Perrier de Fermat (1601-1665) when reading In 1637 the book Diophantus «Arithmetic». In general, there is no need to present such a well-known theorem, its idea is quite simple, even to the student, but the proof was extremely difficult. Fermat’s grand theorem is by no means an example of exciting story about courage, fraud, conjecture, and tragedie - a story that dulls some mathematician of some time. The essence of our proposed method of proof for the particular case n=4 consists in choosing new variables u and v, whose squares are equal to twice the product of the difference or the sum of squares that do not have common divisors, the original variables, respectively. The advantage of the proposed method for n=4 is its simplicity. We hope that a new approach to the proof makes it possible for senior schoolchildren to understand the fate of the theorem more easily, and for the general public of mathematicians to look at the old problem in a new way.