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)
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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).
1/48 + 2/48 = 3/48 = 1/16
1/64 + 3/64 = 4/64 = 1/16
1/80 + 4/80 = 5/80 = 1/16
2/80 + 3/80 = 5/80 = 1/16
1/96 + 5/96 = 6/96 = 1/16
2/96 + 4/96 = 6/96 = 1/16
This could go on forever. There is no final example.
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