摘要
设r是大于1的正奇数,m是偶数。设U_r,V_r是适合V_r+U_r(-1)^(1/2)/=(m+(-1)^(1/2))~r的整数,又设a=│V_r│,b=│U_r│,c=m^2+1。证明了:当a≡2(mod 4),b≡3(mod 4);m≥41r^(3/2)时,方程a^x+b^y=c^2仅有正整数解(x,y,z)=(2,2,r)。
Let r be an odd integer with r>1, and let m be an even integer. Let a=|Vr|,b=|Ur|, c=m2+1, where Ur, Vr are integers satisfying V,+ Ur-1 = (m+-1)r. It will be prowed that if a=2(mod 4), b=3(mod 4) and m>41r3/2, then the equation ax+by=cz has only the positive integer solution (x,y,z)=(2, 2, r).
出处
《黑龙江大学自然科学学报》
CAS
2003年第2期10-14,共5页
Journal of Natural Science of Heilongjiang University
基金
Supported by the National Natural Science Foundation of China(10271104)
the Guangdong Provincial Natural Science Foundation(011781)
the Natural Science Foundation of Education Department of Guangdong Province(0161)