Related papers: Hasse theorem -- an elementary approach

We give a proof of an infinitary version of the well known Hales-Jewett theorem on finite words avoiding the use of ultrafilters.

In this paper we present a short and elementary proof for the error in Simpson's rule.

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.

The paper consists of two parts. The aim of the first, and main, part is to explain, in an elementary way, Hasse's proof of Ramanujan-Nagell's Theorem. In the second part, we formulate some natural extensions of Ramanujan-Nagell's equation.

We prove several extensions of the Erdos-Fuchs theorem.

We illustrate the concept of mathematical proof.

We provide a short proof of the 1-dimensional flat chain conjecture.

In this article we develop counterexamples to the Hasse principle using only techniques from undergraduate number theory and algebra. By keeping the technical prerequisites to a minimum, we hope to provide a path for nonspecialists to this…

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

Equivalencies of many basic elementary inequalities are given

By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We show that, if PA has no non-standard models, then P=/=NP. We then give an elementary proof that PA has no non-standard models.

We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.

We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform…

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.