Lotka’s law describes the frequency of publication by authors in a given field. It states that X^aY = b, where X is the number of publications, Y the relative frequency of authors with X publications, and a and b are constants (with b > 0) that depend on the specific field. Assume that we have data points (X_i,Y_i), i = 1, . . . ,m, and seek to estimate the constants a and b.

1. Show how to find the values of a, b according to a linear least squares criterion. Make sure to define precisely the least-squares problem involved.
2. Is the solution always unique? Formulate a condition on the data points that guarantees unicity.