Павля Кантелли
Мудрец
(14547)
1 год назад
x^30 + x^15 + x^5 + 1 = (x^10 + x^5 + 1)(x^20 + x^15) + x^5 + 1;
x^10 + x^5 + 1 = (x^5 + 1) x^5 + 1;
НОД = 1;
1 = x^10 + x^5 + 1 + (x^5 + 1) x^5 =
x^10 + x^5 + 1 + [x^30 + x^15 + x^5 + 1 + (x^10 + x^5 + 1)(x^20 + x^15)] x^5 =
x^5 (x^30 + x^15 + x^5 + 1) + (x^25 + x^20 + 1) (x^10 + x^5 + 1)