Question

(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)(a^32+1) решите пожалуйста

Answer 1

(a+1)(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)=
=(a+1)·(a-1)/(a-1)·(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)=
=1/(a-1)·(a²-1)(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)=
=1/(a-1)·(a⁴-1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)=1/(a-1)·(a⁸-1)(a⁸+1)(a¹⁶+1)(a³²+1)=
=1/(a-1)·(a¹⁶-1)(a¹⁶+1)(a³²+1)=1/(a-1)·(a³²-1)(a³²+1)=(a⁶⁴-1)/(a-1);