The Non-primitive Solutions of the Equation (x~2+y~2)/(xy+1)~(1/2)=k
LE Mao-hua · Hainan Daxue xuebao. Ziran kexue ban · 2008
In this paper,using the properties of Pell's equation,author proves that,for any positive integer k with k1,the equation (x~2+y~2)/(xy+1)~(1/2)=k has infinitely many positive integer solutions(x,y).Moreover,if k is a prime,then all non-primitive solutions of the equation are given.