MathDB

x

is a positive rational number, show that

x

can be uniquely expressed in the form

x=a_{1}+\frac{a_{2}}{2!}+\frac{a_{3}}{3!}+\cdots,

where

a_{1}a_{2},\cdots

are integers,

0 \le a_{n}\le n-1

for

n>1

, and the series terminates. Show also that

x

can be expressed as the sum of reciprocals of different integers, each of which is greater than

10^{6}

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