A theorem of Erdos states:

"There exists an absolute constant c such that, if n>ck, and if a₁/b₁, a₂/b₂, ... are the Farey fractions of order n, then a_x/b_x and a_x+kb_x+k are similarly ordered."

Can someone provide a definition of "similarly ordered" as used here?

Thanks for any insight.

Cheers, Scott

A theorem of Erdos states:

"There exists an absolute constant c such that, if n>ck, and if a₁/b₁, a₂/b₂, ... are the Farey fractions of order n, then a_x/b_x and a_x+k/b_x+k are similarly ordered."

Can someone provide a definition of "similarly ordered" as used here?

Thanks for any insight.

Cheers, Scott

@ARTICLE{Erdos:1943, author={Erd{"o}s, Paul}, title={A note on {F}arey series}, journal={Quart. J. Math., Oxford Ser.}, fjournal={The Quarterly Journal of Mathematics. Oxford. Second Series}, volume={14}, year={1943}, pages={82--85}, issn={0033-5606}, mrclass={40.0X}, mrnumber={MR0009999 (5,236b)}, mrreviewer={G. Szeg{"o}}