Unsolved Conjectures about Egyptian Fractions

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A unit fraction has numerator 1, as in . An Egyptian fraction is a sum of unit fractions, usually distinct. For example, .


Erdös and Straus conjectured that always has a solution over integers for .

Sierpinski conjectured that always has a solution over integers for .

All have been verified for the Erdös–Straus conjecture [1], but both are still unsolved problems. The Rhind Papyrus and the Egyptian leather scroll solve many similar problems, so these can be considered among the oldest unsolved mathematical problems.


Contributed by: Ed Pegg Jr (December 2013)
Open content licensed under CC BY-NC-SA




[1] A. Swett, "The Erdos–Strauss Conjecture." (Oct 28, 1999) math.uindy.edu/swett/esc.htm.

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