Maybe I am wrong but suppose that (e-pi)^3 is not transcental
It means that (e-pi)^3 is solution of a polynomial equation with integer coefficients
Then
Then e-pi is solution of
Which is not possible because e-pi is supposed transcendental
If e-pi is transendental over Q, how can i show that
e^3 -3e^2.pi + 3e.pi^2 -pi^3 is transendental over Q.
I guess you start off by assuming e-pi is algebraic, but then i dont know how to go about it. Also if i factorise e^3 -3e^2.pi + 3e.pi^2 -pi^3 i get (e-pi)^3. Need help from here, thanks.