A unit fraction is a fraction of the form 1 n where n is a positive integer. Note that the unit fraction 1 11 can be written as the sum of two unit fractions in the following three ways: 1 11 = 1 12 + 1 132 = 1 22 + 1 22 = 1 132 + 1 12 . Are there any other ways of decomposing 1 11 into the sum of two unit fractions? In how many ways can we write 1 60 as the sum of two unit fractions? More generally, in how many ways can the unit fraction 1 n be written as the sum of two unit fractions? In other words, how many ordered pairs (a, b) of positive integers a, b are there for which 1 /n = 1 /a + 1 /b ?
