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Splitting Fractions in "Two"


2/5 can be written as the sum of two unique unit fractions. For example, 2/5 = 1/3 + 1/15. Try to find two unique unit fractions whose sum is 2/7. What about 2/11? 2/13? Is there a pattern?

(Source: Herb Wills, School Science and Mathematics.)




 Extensions


Consider all fractions of the form

where n is a positive integer. Which fractions of this form may be expressed as the sum of two different unit fractions?


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