摘要
设m是正偶数.运用初等数论方法证明了:当m≡2(mod 4)时,方程|m(m^6-21m^4+35m^2-7)|~x+|7m^6-35m^4+21m^2-1|~y=(m^2+1)~z仅有正整数解(x,y,z)=(2,2,7).并且指出了相关文献中的一个不足之处.
Let m be an even positive integer. Using certain elementary number theory methods,we prove that if m≡ 2(mod 4),then the equation |m(m6-21 m4 + 35 m2-7)|^x +|7 m6-35 m4 + 21 m2-l|^y =(m^2 + 1)^z has only the positive integer solution(x,y,z)=(2, 2, 7).Moreover, an error of reference No.9 is pointed.
作者
吴华明
WU Hua-ming(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China)
出处
《数学的实践与认识》
北大核心
2019年第2期259-264,共6页
Mathematics in Practice and Theory
基金
岭南师范学院重点学科项目(1171518004)
