【摘要】 运用初等数论方法和四次Diophantine方程的结论讨论了不定方程vk=s2±1的可解性,并给出该方程的所有正整数解(k,s),其中vk=αn-αn/α-α,k是任意非负整数,α=a+a2-1(1/2),α=a-(a2-1)(1/2),a>1为固定的正整数.更多还原

【Abstract】 By using the elementary number theory methods and some results on the number of quartic Diophantine equations,the solvability of the indeterminate equation vk=s2±1is discussed,and its all positive integer solution(k,s)are completely determined,where vk=αn-αn/α-α,k is any nonnegative integer,α=a+(a2-1)(1/2),α=a- (a2-1)(1/2),ais a fixed positive integer with a>1.更多还原