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 ax/bx and ax+k/bx+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}}



Similarly Ordered
Here is a link that gives the definition: <http://qjmath.oxfordjournals.org/cgi/pdf_extract/os-13/1/185>


It's to the paper by Mayer that Erdos refers to. (The link gives you just the first page of the paper, but fortunately the definition is on that page.)


