let k >= 2 show that n= 5^k-1 satisfies the equation 4σ(n) = 5n-1

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t)-(3t+ 9) (+8t+7)^. (a) Find the total profit in the first four years. (b) Find the profit in the fifth year of operation. (c) What is happening to the annual profit over the long run? (a) The total profit in the first four years is $ (Round to the nearest dollar as needed.). CUP

For a positive integer n, prove that summation d/n mu^(2)(d) phi(d) = n / phi(n). [Hint: Both sides of the equation are multiplicative functions].

Question 54 please