I am doing a presentation over the pell equation and specifically the pigeonhole argument....I am getting hung up on proving Dirichlet's approximation theorem...my professor wrote out the proof for me and I am not following the way he did it..everyone is so good about explaining stuff on this forum I figured I would post and hope someone knows how to do this..

Dirichlet's approximation theorem:

for any irrational sqrt(n) and integer B>0 there are integers a, b with

0<b<B and

| a - b(sqrt(n)) | < 1/B

Hopefully the proof of whoever helps will be alot clearer than my professors