# Revision history [back]

Hi, here is my code

%time
var('n,R,T')
eq1 = ((n-1)^2/(n+1)^2)==(-1-2*R+R^2-T^2+sqrt(4*T^2+(1-2*R+R^2-T^2)^2))/(2*R-4)
sol=solve(eq1,n,solution_dict=true)
test1 = (eq1.substitute(n=sol[0][n]))
test2 = test1.lhs()-test1.rhs()
test3 = expand(test2).full_simplify()
test3


and the glorious result

0
CPU time: 4575.08 s,  Wall time: 4601.30


I would like to thank DSM for pointing out that my previous attempt would not result into an integer and John Palmieri to extend the usable memory for the virtual machine.

Hi, here is my code

%time
var('n,R,T')
eq1 = ((n-1)^2/(n+1)^2)==(-1-2*R+R^2-T^2+sqrt(4*T^2+(1-2*R+R^2-T^2)^2))/(2*R-4)
sol=solve(eq1,n,solution_dict=true)
test1 = (eq1.substitute(n=sol[0][n]))
test2 = test1.lhs()-test1.rhs()
test3 = expand(test2).full_simplify()
test3


and the glorious result

0
CPU time: 4575.08 s,  Wall time: 4601.30


I would like to thank DSM for pointing out that my previous attempt would not result into an integer and John Palmieri to extend the usable memory for the virtual machine.

Since this is a very special question and I got an answer now, should I delete it or which answer should get the answer check?