Question

已知数2的50次方—4的17次方能被60至70之间的两个数整除,这两个数是

Answer 1

2^50-4^17

=2^50-2^34

=2^34(2^16-1)

=2^34*(2^8+1)(2^8-1)

=2^34*(2^8+1)*(2^4+1)(2^4-1)

=2^34*(2^8+1)*17*15

=2^32*(2^8+1)*(2^2*17)*15

=2^26*(2^8+1)*(2^2*17)*2^6

=2^24*(2^8+1)*15*68*64

所以是64和68