Related papers: A new proof of Vantieghem's 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 the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.
In this paper we present four necessary and sufficient conditions for a natural number to be prime.
In this note we present a family of congruences which hold if and only if a natural number $n$ is prime.
We strengthen the Free Will Theorem, which proved the spontaneity of particles, based on the free will of the experimenter. The new result is unconditional, and does not require the experimenter's free will to prove the particles'…
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
Alpoge and Granville (separately) gave novel proofs that the primes are infinite that use Ramsey Theory. In particular, they use Van der Waerden's Theorem and some number theory. We prove the primes are infinite using an easier theorem from…
The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure…
We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.
We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
We give a counting based proof of the Graham Pollak Theorem
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…
I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…
We show that Leonardo da Vinci's well known proof of the Pythagorean theorem is due to Mayer and not to da Vinci.
In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
Theorem proving is one of the oldest applications which require heuristics to prune the search space. Invertible proof procedures has been the major tool. In this paper, we present a novel and powerful heuristic called $nongshim$ which can…