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单词 AdjacentFraction
释义

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:

ab-cd=1n.

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

111-112=1132.

117 and 119 are not since:

117-119=2323.

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

2019-1919=119.

or unit fractions:

34-23=112.

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:

170+171=1414970.
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更新时间:2025/5/4 12:24:42