Применение некоторых моментов, не имеющих распространения в современной алгебре и теории чисел, по крайней мере в справочной литературе, для доказательства теоремы Ферма и гипотезы Била.

The purpose of this work is to prove Beal's conjecture. The proof is based on methods not currently used by elementary mathematics. The concept of them is absent in the reference sources. Firstly, this is an idea of the possibility of expressing an even number that has a factor of 8 by the difference of the squares oftwo odd numbers. In addition, a feature of the integer solution of the quadratic equation by Pythagorean triples is applied. As a result, Beale's conjecture was completely proved, taking into account the accompanying Fermat's Last Theorem, by simple methods. Keywords: difference of squares of two odd numbers, factorization, even numbers, odd numbers, Pythagorean triples.