adjacent fraction
Two fractions and , of the positive integers are adjacent if their difference is some unit fraction , that is, if we can write:
For example the two proper fractions and unit fractions and are adjacent since:
and 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 of a degree are always adjacent fractions. In the first Farey sequence of a degree 1 there are only two adjacent fractions, namely and .
Adjacent unit fractions can be parts of many Egyptian fractions: