Suppose a, b and c are three distinct natural numbers such that a + b + c = abc. Consider the following statements : 1. The arithmetic mean of a, b and c is a natural number. 2. The harmonic mean of a, b and c lies between 1 and 2. Which of the statements given above is/are correct?

The equation a + b + c = abc for distinct natural numbers has only one unique solution set: {1, 2, 3}. To see this, assume a < b < c; then abc = a + b + c < 3c, which implies ab < 3. Since a and b are distinct natural numbers, the only possibility is a = 1 and b = 2, which yields c = 3. For statement 1, the Arithmetic Mean (AM) is (1 + 2 + 3) / 3 = 6 / 3 = 2, which is a natural number. For statement 2, the Harmonic Mean (HM) is 3 / (1/a + 1/b + 1/c). Substituting the values, HM = 3 / (1/1 + 1/2 + 1/3) = 3 / (11/6) = 18/11. Since 18/11 is approximately 1.636, it lies strictly between 1 and 2. General properties of AM and HM are discussed in mathematical literature. Thus, both statements are correct.