Hence R^2(X-3)=(X^2+1)p^2(X-3)-1. So, it is enoung to find all f and g with integer coefficients such that (X^2+1)f^2(X)=g^2(X)+1. We will use the following result: all positive integer solutions of the Pell equation x^2+1=2y^2 are given by x_n=1/2((1+sqrt(2)^(2n-1)+(1-sqrt(2))^2n-1) and y_n=1/(2sqrt(2)((1+sqrt(2)^(2n-1)-(1-sqrt(2))^(2n-1)).
Kaya R ^ 2 (X-3) = (X ^ 2 +1) p ^ 2 (X-3) -1. Kaya, ito ay enoung upang hanapin ang lahat ng f at g sa integer coefficients tulad na (X ^ 2 +1) f ^ 2 (X) = g ^ 2 (X) 1.