因式分解 x^3-3x-2 求证2^48-1可以被63和65整除
2个回答

x^3-3x-2

=x^3-x-2x-2

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

=x(x-1)(x+1)-2(x+1)

=(x+1)[x(x-1)-2)

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

=(x+1)(x-2)(x+1)

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

63=64-1=2^6-1

65=64+1=2^6+1

(2^48-1)

=(2^24+1)(2^24-1)

=(2^24+1)(2^12+1)(2^12-1)

=(2^24+1)(2^12+1)(2^6+1)(2^6-1)

(2^-48-1)/63=(2^24+1)(2^12+1)(2^6+1)

(2^-48-1)/65=(2^24+1)(2^12+1)(2^6-1)

2^48-1可以被63和65整除