# A Simple Proof of a Curious Congruence by Sun

## Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1289-1291 window.___gcfg = {lang: 'ko'}; (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/platform.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

Author :

Abstract : In this note, we give a simple and elementary proof of the following curious congruence which was established by Zhi-Wei Sun: $\sum_{k=1}^{(p-1)/2}\frac{1}{k\cdot 2^{k}}\equiv \sum_{k=1}^{[3p/4]}\frac{(-1)^{k-1}}{k}\quad (\text{mod}\,p)$ .

Keyword : Primary 11A07, 11A41

## Representing Quasi-Orders by Embeddability Ordering of Families of Topological ..

An elementary argument constructs, for each cardinal $\alpha$ , a topological space whose ..

## On Swan Conductors for Brauer Groups of Curves Over Local Fields

For an element w of the Brauer group of a curve over a local field, we define the Swan conduc..

## The Ideal of Polynomials Vanishing on a Commutative Ring

We determine equivalent conditions on a commutative Artinian ring S in order that the ideal o..

## Conical Limit Set and Poincare Exponent for Iterations of Rational Functions

We contribute to the dictionary between action of Kleinian groups and iteration of rational f..

## A Gauss-Kusmin Theorem for Optimal Continued Fractions

A Gauss-Kusmin theorem for the Optimal Continued Fraction (OCF) expansion is obtained. In ord..

## Local Tomography with Nonsmooth Attenuation

Local tomography for the Radon transform with nonsmooth attenuation is proposed and justified..

## Simple Families of Thue Inequalities

We use the hypergeometric method to solve three families of Thue inequalities of degree 3, 4 ..

## Criteria of Algebraic Independence with Multiplicities and Interpolation Determ..

We generalize Gelfonds criterion of algebraic independence by taking into account the values ..

## The treatment of movement disorders using Gamma Knife stereotactic radiosurgery..

In this era of modern neurosurgery, we are able to provide adequate amelioration of disabling s..

## The role of radiosurgery for glial neoplasms.

Malignant gliomas are one of the most serious challenges in clinical neurosurgery. Despite adva..