1. Find three irreducible fractions with numerators and denominators not equal to 1, such that their sum is an integer, and the sum of the fractions reciprocal to them is also an integer.
Solution. For example, 11/2, 11/6, 11/3. Remark. The problem setters, of course, meant that the fractions should be different. But since this was not explicitly stated in the problem, answers with equal fractions, such as $-1 / 3,-1 / 3,-1 / 3 ; 5 / 2,5 / 4,5 / 4$ and so on, are also accepted.