MathDB
F 7

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May 25, 2007
searchrational numbers

Problem Statement

If xx is a positive rational number, show that xx can be uniquely expressed in the form x=a1+a22!+a33!+⋯ ,x=a_{1}+\frac{a_{2}}{2!}+\frac{a_{3}}{3!}+\cdots, where a1a2,⋯a_{1}a_{2},\cdots are integers, 0≤an≤n−10 \le a_{n}\le n-1 for n>1n>1, and the series terminates. Show also that xx can be expressed as the sum of reciprocals of different integers, each of which is greater than 10610^{6}.
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