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sage: _.<x> = GF(2^8, 'a')[]
sage: P = x^8 + x^7 + x^5 + x^3 + 1
sage: P.roots()
[(a^5 + a + 1, 1),
(a^6 + a^5 + a^4 + 1, 1),
(a^6 + a^5 + a^4 + a^2 + a, 1),
(a^6 + a^5 + a^4 + a^3 + a, 1),
(a^7 + a^5 + a^2 + 1, 1),
(a^7 + a^5 + a^3 + a, 1),
(a^7 + a^5 + a^4, 1),
(a^7 + a^6 + a^5, 1)]
