(a) Find the positive integers m, n such that $$\frac{1}{m} + \frac{1}{n} = \frac{3}{17}$$. Also find the positive integers m, n, p such that $$\frac{1}{m} + \frac{1}{n} + \frac{1}{p} = \frac{3}{17}$$. Using this idea, prove that for any positive integer k we can find k distinct integers $$n_1, n_2, \ldots, n_k$$ such that $$\frac{1}{n_1} + \frac{1}{n_2} + \ldots + \frac{1}{n_k} = \frac{3}{17}$$.