Related papers: An Elementary proof for Bertrand's Postulate
We provide a simple proof of Kamp's theorem.
This is an expository article on relating the Chebotarev Density Theorem to the Bateman-Horn constant.
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
We give a new proof of Lucas' Theorem in elementary number theory.
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.
Consider an algebraic number field, $K$, and its ring of integers, $\mathcal{O}_K$. There exists a smallest $B_K>1$ such that for any $x>1$ we can find a prime ideal, $\mathfrak{p}$, in $\mathcal{O}_K$ with norm $N(\mathfrak{p})$ in the…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
A simple proof of Atanassov's Conjecture is presented. Atanassov's Conjecture is a generalization of Sperner's Lemma, a lemma which has been used to prove Brouwer's Fixed Point Theorem, among other fixed point theorems. The proof of…
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .
We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…
We introduce an elementary argument to the theory of distribution of sequences modulo one.
Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is…