关于丢番图方程x^4+my^4=z^4  

About the Diophantine Equation X + mY4= Z

作　　者：熊文[1] 

机构地区：[1]广西交通职业技术学院,广西南宁530023

出　　处：《南宁师范高等专科学校学报》2003年第1期43-46,共4页Journal of Nanning Junior Teachers College

摘　　要：利用初等数论方法及Fermat无穷递降法,证明了丢番图方程x^4+my^4=z^4,在m=12,-48,42,-168时均无正整数解;在m=-12,-42,48,168时均有无穷多组正整数解,并进一步得出了其解的通解公式,从而获得了Tijdeman猜想与广义Fermat猜想的进一步结果。With the use of approach of elementary number theory and Fermat's infinite decrease by degrees, it proves that if m = 12, -48, 42, -168, the diophantine equation X4 + mY4 = Z2 has no positive integer solutions; if m = -12, -42, 48, 168, then the equation has infinite integer solutions. And we can also draws its solutions' common formula, and gets the further results of Tijdeman's conjecture and the General Fermat's conjecture

关 键 词：丢番图方程 初等数论 通解公式 TIJDEMAN猜想 广义FERMAT猜想 FERMAT无穷递降法 

分 类 号：O156.7[理学—数学]