摘要
利用初等数论相关内容与运算技巧,探究了一个包含常数项的系数为特殊勾股数的三元变系数欧拉函数方程的可解性.在之前的多次累计运算中发现,当方程中的系数越大时,运算过程冗长且后面的情况几乎无解,故在方程中添加了调和数,使得运算过程得到了最大程度的精简.添加常数项对此类运算提供了很好的精简思路,最后给出了该方程的17组正整数解.
In this paper,the solvability of a ternary variable coefficient Euler function equation with a constant term whose coefficient is a special Pythagorean number is investigated by using the relevant contents and operational technigues of elementary number theory.In the previous multiple accumulative operations,it is found that when the coefficients in the equation are larger,the operation process is lengthy and there is almost no solution in the following cases.Therefore the harmonic number is added to the equation,which makes the operation process to the maximum degree of simplification.Adding constant term provides a good way to simplify the operation of this kind.Finally,17 sets of positive integer solutions to the equation are given.
作者
张明丽
高丽
ZHANG Mingli;GAO Li(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,Shaanxi China)
出处
《河南科学》
2020年第3期351-355,共5页
Henan Science
基金
国家自然科学基金资助项目(11471007)
陕西省科技厅科学技术研究发展计划资助项目(2013JQ1019)
延安大学校级科研计划资助项目(YD2014-05)
延安大学研究生教育创新计划项目(YCX201901)。
关键词
EULER函数
勾股数
不定方程
正整数解
Euler function
Pythagorean number
indeterminate equation
positive integer solution
