3^227-27可以被25和30之间某3个数整除,这三个数是

Question

3^227-27可以被25和30之间某3个数整除,这三个数是

Answer 1

3^227-27可以被25和30之间某3个数整除,这三个数是 :26 ,27 ,28
3^227-27
=3^227-3³
=27×(3^224-1)
=27×(3^112-1)(3^112+1)
=27×(3^56-1)(3^56+1)(3^112+1)
=27×(3^28-1)(3^28+1)(3^56+1)(3^112+1)
=27×(3^14-1)(3^14+1)(3^28+1)(3^56+1)(3^112+1)
=27×(3^7-1)(3^7+1)(3^14+1)(3^28+1)(3^56+1)(3^112+1)
=27×728×(3^7+1)(3^14+1)(3^28+1)(3^56+1)(3^112+1)
=27×26×28×(3^7+1)(3^14+1)(3^28+1)(3^56+1)(3^112+1)