Mersenne: Basic question: Working modulo 2^n-1

[Foghorn Leghorn]

Chris Caldwell's web page on Mersenne numbers descirbes the Lucas-Lehmer 
test briefly and mentions that it is quick on binary computers because 
they can quickly perform division by 2^n-1. I know how to find integer 
quotients and remainders modulo 2^n with shifting and masking, but I 
don't understand how it is done quickly modulo 2^n-1. Would anyone care 
to explain?

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