Question

帮忙解下(2+1)(2^2+1)(2^4+1)……(2^32+1)+1

Answer 1

解：原式 = (2-1)(2+1)(2^2 +1)(2^4 +1)............(2^32 + 1) + 1 = (2^2 - 1 )(2^2 + 1 )(2^4 + 1).........(2^32 + 1) + 1 =(2^4 -1)(2^4 + 1) ........【反复运用平方差公式】 ............... = 2^64 -1 + 1 = 2^64

Answer 2

(2+1)(2^2+1)(2^4+1)……(2^32+1)+1 =(2-1)(2+1)(2^2+1)(2^4+1)……(2^32+1)+1 =(2^2-1)(2^2+1)(2^4+1)……(2^32+1)+1 =(2^4-1)(2^4+1)……(2^32+1)+1 =2^64-1+1 = 2^64