FU Ruiqin1,2, YANG Hai1,3*, ZHANG Jianhua1
(1 College of Mathematics and Information Science,Shaanxi Normal University, Xi′an 710119, Shaanxi, China;2 College of Science, Xi′an Shiyou University, Xi′an 710065, Shaanxi, China;3 College of Science, Xi′an Polytechnic University, Xi′an 710048, Shaanxi, China)
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±1 is discussed, and its all positive integer solution (k,s) are completely determined, where vk=αn-nα-,k is any nonnegative integer,α=a+a2-1,=a-a2-1,a is a fixed positive integer with a>1.
KeyWords:
Lucas sequence; near square; quartic Diophantine equation
