Problem: Sum of Unit Fractions (click here to see the problem statement)

My Solution. We are looking for

where , , and



We have,



If we let ,




Which implies that :


Which can only be true when , so

Using the relationship , I set up a table




So the answer to the question,

"Which of these fractions (, where n is a positive integer) may be expressed as the sum of two different unit fractions of integers?" appears to be: ALL OF THEM.