﻿ M角数恒等式及其应用—从M角数谈起 The Identities of M-Gonal Number with Its Application—M-Gonal Numbers Revisited

Pure Mathematics
Vol.07 No.04(2017), Article ID:21264,5 pages
10.12677/PM.2017.74032

The Identities of M-Gonal Number with Its Application

—M-Gonal Numbers Revisited

Minghao Guo1, Zhicheng Guo2

1School of Biomedical Engineering, Shanghai Jiaotong University, Shanghai

2Dept. Northern Design and Research Institute, Shijiazhuang Hebei

Received: Jun. 17th, 2017; accepted: Jun. 30th, 2017; published: Jul. 6th, 2017

ABSTRACT

In this paper, we present some arithmetic relationships among same-level M-Gonal numbers in a specific situation. We also illustrate some arithmetic relations on M-Gonal numbers who are related with Pythagorean Triangles Number. A few special cases are discussed to obtain some interesting results.

Keywords:M-Gonal Number, Pythagorean Equation, Partitions

M角数恒等式及其应用

—从M角数谈起

1上海交通大学生物医学工程学院，上海

2北方设计研究院，河北 石家庄

1. 引言

Fermat在Diophtantus的《数论》的空白处写下了第18条评注是下面的命题 [1] 。

Euler在知道了Fermat的命题1时颇为激动，然而对命题2的证明颇费周章却不得其解。1772年Lagrange在Euler研究的基础上，利用Euler的四平方恒等式 [2]

134角数等于第124角数与第54角数之和。

2. 应用简介

3. 一般的整数分拆命题

4. 分拆理论现状简介及展望——用多个平方和表示的数

The Identities of M-Gonal Number with Its Application—M-Gonal Numbers Revisited[J]. 理论数学, 2017, 07(04): 250-254. http://dx.doi.org/10.12677/PM.2017.74032

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10. NOTES

1M角数是所有角数的统称，m角数指角数为m的数列。

2本结论将指数2推广到了任意正整数(偏序集)。当结论用于平面直角三角形时，就是勾股定理。当指数s取无穷大时，就是圆周长公式

3由于洛伦兹(Lorentz)变换是相对论的数学工具，从M角数的平面图可以看出，结论给出的是研究量子理论的数学工具。故称之为洛伦兹(Lorentz)变换的对偶定理