Related papers: A new proof of Lucas' Theorem

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…

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $\sigma$-algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove…

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

We will give a simple proof of the ambiguous class number formula.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We give a new proof of Chen-Lin result with Li-Zhang method.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We prove a new cross theorem for separately holomorphic functions.

We prove the decidability of the elementary theory of a free group.

We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

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.