Related papers: A new proof of Lucas' Theorem
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
A very simple but useful almost sure convergence theorem of probability is given.
In this short paper, we prove, by only using elementary tools, general cases when $U_n(P,Q) \neq \square$, where $U_n(P,Q)$ is the Lucas sequence of the first type.
We present an elementary proof for Ljunggren equation
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.
In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…
We give a proof of the geometric fundamental lemma of Kottwitz. As explained by Laumon, this implies the fundamental lemma for the unitary groups.
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
A vector variational principle is proved.
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We also apply some lemmas to prove the Pizza Theorem.
We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.
We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$