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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)