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#### conscipost

##### Member

- Jan 26, 2012

- 39

Is it necessary for a unit sum composed of unit fractions to include 1/2? Doing maple runs this seems to be the case, but it is not evident to me how this could be

Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia

But considering an arbitrary fraction and one minus it, it seems the unit fraction representation of one of these two's parts is bound to include 1/2.

I feel a bit mixed up here.

EditEdit:1/3+1/4+1/5+1/6+1/20 does it. I think I thought that distinct unit fraction representations were unique. But this is not the case clearly.

Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia

But considering an arbitrary fraction and one minus it, it seems the unit fraction representation of one of these two's parts is bound to include 1/2.

I feel a bit mixed up here.

EditEdit:1/3+1/4+1/5+1/6+1/20 does it. I think I thought that distinct unit fraction representations were unique. But this is not the case clearly.

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