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A unit fractionis a fraction of the form 1/n for some nonzero integer n. Compute the number of ways we can write 1/16 as the sum of two distinct positive unit fractions. (The order of the fractions in the sum does not matter, so 1/2+1/3 would be considered the same sum as 1/3+1/2)

 Jan 12, 2022
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A unit fractionis a fraction of the form 1/n for some nonzero integer n. Compute the number of ways we can write 1/16 as the sum of two distinct positive unit fractions. (The order of the fractions in the sum does not matter, so 1/2+1/3 would be considered the same sum as 1/3+1/2)  

 

Well, there are

 

1/32 + 1/32 

1/64 + 3/64 

1/128 + 7/128 

 

We could keep doubling the denominator indefinitely, so I conclude there is no end to it.  

 

Not to mention 

 

1/48 + 2/48  

1/96 + 5/96 

1/192 + 11/192 

 

And we could keep doubling that denominator as well.  

.

 Jan 12, 2022

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