adjacent fraction

Two fractions ab and cd, ab>cd of the positive integers a,b,c,d are adjacent if their difference is some unit fractionPlanetmathPlanetmath 1n, n>0 that is, if we can write:


For example the two proper fractions and unit fractions 111 and 112 are adjacent since:


117 and 119 are not since:


It is not necessary of course that fractions are both proper fractions:


or unit fractions:


All successive terms of some Farey sequence Fn of a degree n are always adjacent fractions. In the first Farey sequence F1 of a degree 1 there are only two adjacent fractions, namely 11 and 01.

Adjacent unit fractions can be parts of many Egyptian fractionsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath:

Title adjacent fraction
Canonical name AdjacentFraction
Date of creation 2013-03-22 12:48:23
Last modified on 2013-03-22 12:48:23
Owner XJamRastafire (349)
Last modified by XJamRastafire (349)
Numerical id 17
Author XJamRastafire (349)
Entry type Definition
Classification msc 11A67
Related topic FareySequence
Related topic UnitFraction
Related topic ContinuedFraction
Related topic NumeratorAndDenominatorIncreasedBySameAmount