Related papers: Fermat's Last Theorem and its another Proof

We present the only proof of Pierre Fermat by descente infinie that is known to exist today. As the text of its Latin original requires active mathematical interpretation, it is more a proof sketch than a proper mathematical proof. We…

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

In this note a far extension of the Banach fixed point theorem is proved.

Comments about the paper by Elsholz, Fermat's last theorem implies Euclid's infinitude of primes, (2021), and simplification.

We give a new proof of Lucas' Theorem in elementary number theory.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We study Fermat's Last Theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions (B,e) of models of arithmetical theories (in the language L=(0,1,+,x,<)) by a binary (partial or total)…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

Let $K$ be a totally real number field. For all prime number $p\geq 5$, let us denote by $F_p$ the Fermat curve of equation $x^p+y^p+z^p=0$. Under the assumption that $2$ is totally ramified in $K$, we establish some results about the set…

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

We provide a simple proof of Kamp's theorem.

It is an original method based on systems of prameters represented by reals which obey to an infinite descent (convergent sequences). We define calculus of quotients and they conduct quickly to a consequent result. Our own scepticism made…

In this note we shall give a new proof to a quadrature formulae due to Newton.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.