The question of ambiguity in mathematics and some of arising from these extraordinary consequences. (Elementary aspect) 2014 (English, Russian)
This paper proposes a complete elementary without reference to other sources (except for Euler), first proof of the Fermat's Last Theorem. We resolve the question of the ambiguous expansion in the Binomial theorem, Resolved the question of the ambiguity certain infinite sequences of the Euler. Given other versions proof of FLT, We consider and solve the question of not available modern geometric representation of continuous functions without derivatives at any point.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 3 No. 4 (2014), pp. 01- 33
The ways of finding uncountable set solutions for equations of....
(Elementary aspect) 2014 (English, Russian)
Now we shall give the variants of uncountable set solutions that are a prime numbers and also a not coprime numbers of the Beal conjecture as well as, the version of anti-solution for the Pillai's conjecture.
INTERNATIONAL FRONTIER SCIENCE LETTERS(IFSL) ISSN:2349-4484Vol. 1 No. 2 (2014), pp. 19-32
Alternative solution of the Beal conjecture including another proof of the Fermat's Last Theorem, without references to the other works in the main part. (Elementary aspect) 2014 (English, Russian)
The aim of this paper is to prove the following possible solutions of the Beal conjecture and another proof of the Fermat’s Last Theorem, without references to the other works in the main part.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 3 No. 1 (2014), pp. 21-28
SOME ANTI-SOLUTIONS OF THE PILLAI'S CONJECTURE AND PROOF OF FERMAT'S LAST THEOREM 2013 (English, Russian)
Let us show several; including the part already well known variants of find uncountable set solutions of equation ,in contrast to the Pillai's conjecture. The proof of Fermat's Last Theorem.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 2 No. 4 (2013), pp. 47-64
One of the principal problems of the Beal's conjecture. The proof of Catalan's Conjecture. 2013 (English, Russian)
First found methods and identities, allowing receiving infinite number solutions of equations.As the solution of the main problem appeared additional problems that solved by obtained appropriate identities. Given as two equal proofs of Catalan's Conjecture.
Bulletin of Society for Mathematical Services and Standards ISSN: 2277-8020 Vol. 2 No. 4 (2013), pp. 01-20
Remarks
The Pythagorean triples whose hypotenuse and the sums of the legs are squares. 2013 (English, Russian)
More than 370 years ago the famous French mathematician Pierre de Fermat proposed to solve the following problem: to find a Pythagorean triples whose hypotenuse and the sum of the legs were squares, which, despite its simplicity, has been very difficult. Problems associated with its solution involved many mathematicians such as (Leonhard Euler, Joseph-Louis Lagrange, Ljnggren, Wacław Sierpiński and etc.) But in the end it did not reach solution. In our article, solution communicated to obtain the equations giving the required values all elements of the Pythagorean triples in positive integers (natural) are co-prime integers, and provides a second solution of this problem (the values of x, y, z of 45 digits), and some consequences.
Bulletin of Society for Mathematical Services and Standards ISSN: 2277-8020 Vol. 2 No. 3 (2013), pp. 60-73
THE PROOF OF THE INSOLUBILITY IN NATURAL NUMBERS FOR THE FERMAT'S LAST THEOREM AND BEAL'S CONJECTURE FOR CO-PRIME INTEGERS ARRANGED IN A PAIR IN THE EQUATIONS...
(ELEMENTARY ASPECT) 2013 (English, Russian)
We give the corresponding identities for different solutions of the equations as for coprime integers, further,for not coprime integers.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 2 No. 3 (2013), pp. 53-60
Proof of Beal's Conjecture
2013 (English, Russian)
We give the complete proof of Beal’s conjecture.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 2 No. 3 (2013), pp. 61-64
THE REPRODUCTIVE SOLUTION FOR FERMAT’S LAST THEOREM
(Elementary Aspect) 2013 (English, Russian)
We give a proof of the solvability in a natural numbers for Fermat’s Last Theorem
has not been found earlier, significantly different from known, and allow us to obtain infinite set of
solutions in natural numbers, and examples.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 2 No. 3 (2013), pp. 05-15
The Identities of Ordinary Which Is Leading to the Extraordinary Consequences (Elementary Aspect) 2013 (English transl)
The identity, allows obtaining range of identities as consequences, giving:
1) The alternative proof of Fermat’s Last theorem, using method of infinite descent, which is with a high degree of probability could be the solution to Fermat and proof of insolubility in natural numbers of equations.
2) Presenting another way of solutions Hilbert's seventeenth problem.
3) Version of proof which is associated with the solution of the Poincare conjecture.
Asian Journal of Mathematics and Applications - ISSN 2307-7743
THE SECOND PROOF OF THE FERMAT'S LAST THEOREM
(ELEMENTARY ASPECT) 2013 (English, Russian)
We give a second proof of Fermat’s Last theorem without reference to the closure of
numerical systems with respect to the operation of superposition.
Bulletin of Mathematical Sciences & Applications ISSN: 2278-9634 Vol. 2 No. 3 (2013), pp. 16-25