Related papers: A new proof of Lucas' Theorem
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A proof is given of Rosenthal's \(\ell_1\) theorem.
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We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…
We survey the classical results on the prime number theorem
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Lucas' theorem describes how to reduce a binomial coefficient $\binom{a}{b}$ modulo $p$ by breaking off the least significant digits of $a$ and $b$ in base $p$. We characterize the pairs of these digits for which Lucas' theorem holds modulo…