简化计算 (2+1)(2^2+1)(2^4+1)(2^8+1)(2^32+1)+1

3个回答

  • 题目中是不是少了(2^16+1)

    (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

    =(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

    =(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

    =(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

    =(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1

    =(2^16-1)(2^16+1)(2^32+1)+1

    =(2^32-1)(2^32+1)+1

    =2^64-1+1

    =2^64

    补充:没有(2^16+1)项这个题目很难化简下去,答案就不是2^64