Докажите неравенство: a) (а-1) (а+1) (a^2+1) (a^4+1) (a^8+1) = a^16-1

б) (b+c) (b^2+c^2) (b^4+c^4) (b^8+c^8) = (b^16-c^16) / b-c (b не равно c)

А) a^16 - 1 = (a^8) ^2 - 1^2 = (a^8 + 1) (a^8 - 1) = (a^8 + 1) (a^4 + 1) (a^4-1) =

= (a^8+1) (a^4+1) (a^4-1) = (a^8+1) (a^4+1) (a2+1) (a^2 - 1) =

= (a^8+1) (a^4+1) (a^2+1) (a+1) (a-1).

б) (b^16 - c^16) / (b - c) = (b^8+c^8) (b^8 - c^8) / (b - c) =

= (b^8+c^8) (b^4+c^4) (b^4 - c^4) / (b - c) =

= (b^8+c^8) (b^4+c^4) (b^2+c^2) (b^2-c^2) / (b - c) =

= (d^8+c^8) (v^4+c^4) (b^2+c^2 ((b+c) (b-c) / (b - c) =

= (b^8+c^8) (b^4+c^4) (b^2+c^2 ((b+c)