形如p^2+(4n(n+1)s^2k^2)/(s^2-1)的平方数

The Squares with the form p^2+(4n(n+1)s^2k^2)/(s^2-1)

设n,p为正整数,k和s>1为奇数,(ks)2-(s2-1)p2为素数,当k|p或(ks,(ks)2-(s2-1)p2)=1时,得到使p^2+(4n(n+1)s^2k^2)/(s^2-1)是平方数的正整数n所满足的条件.

Let nand p be positive integers, let s be a positive odd integer with s 〉 1, and let k be a positive odd integer, Let （ks） 2 - （ s2- 1 ）p2 be a prime, when k is divisible by p or （ ks, （ks） 2 - （ s2 - 1 ） p2 ） = 1, In this paper, all positive integers n which makes the form p2＋4n（n＋1）s2k2/s2-1 to be a square were given.