4912.sagews

x=var('x')
for i in range(10):
    n=2^i
    print x^n
    print " ->",factor(x^n-1)

x -> x - 1 x^2 -> (x - 1)*(x + 1) x^4 -> (x - 1)*(x + 1)*(x^2 + 1) x^8 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1) x^16 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1) x^32 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1) x^64 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1)*(x^32 + 1) x^128 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1)*(x^32 + 1)*(x^64 + 1) x^256 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1)*(x^32 + 1)*(x^64 + 1)*(x^128 + 1) x^512 -> (x - 1)*(x + 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1)*(x^32 + 1)*(x^64 + 1)*(x^128 + 1)*(x^256 + 1)