Wednesday 22 November 2006

nt.number theory - Similarly Ordered

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}}

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