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)
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.
.