3*5*17*(2^8+1)简便方法计算,40又2/3*39又1/3

1个回答

  • 3*5*17*(2^8+1)

    =3*5*17*(2^8+1)(2^8-1)*除以(2^8-1)

    =3*5*17*(2^8+1)(2^8-1)*除以[(2^4-1)(2^4+1)]

    =3*5*17*(2^8+1)(2^8-1)*除以[(2^2-1)(2^2+1)(2^4+1)]

    =3*5*17*(2^8+1)(2^8-1)*除以[(2-1)(2+1)(2^2+1)(2^4+1)]

    =3*5*17*(2^8+1)(2^8-1)*除以[1*3*5*17]

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

    =2^16-1

    =65535

    40又2/3*39又1/3

    =(40+2/3)(40-2/3)

    =40^2-(2/3)^2

    =1600-4/9

    =1599又5/9