摘要
设m为正整数,且a=m7-21m5+35m3-7m,b=7m6-35m4+21m2-1,c=m2+1.本文同时利用2个代数数的线性型下界估计以及2个有理数方幂之差的p-adic值的下界估计的一些深入结果,证明了对正整数m≥2.4×109,丢番图方程ax+by=cz仅有正整数解(x,y,z)=(2,2,7).
In our report, let m ∈n,a =m^7 -21m^5 +35m^3 -7m,b =7m^6 -35m^4 +21m^2 - 1 ,c =m^2 + 1, A deep result of the lower bound for linear forms in two logarithms and the lower bound for the p-adic distance between two powers of rational numbers were used to prove that if m≥2. 4 x 109, the Diophantine equation a^x + b^y = c^z has only one positive integer solution (x,y,z) = (2,2,7).
出处
《海南大学学报(自然科学版)》
CAS
2012年第4期309-315,共7页
Natural Science Journal of Hainan University
基金
西华师范大学大学生科技创新基金项目(42711114)
关键词
丢番图方程
TERAI猜想
正整数解
对数线性型
p-adic标准值
Diophantine equation
Terai conjecture
positive interger solution
linear forms in two logarithms
p-adic standard value