1. Write a program which prompts for two positive integers and then prints their least common multiple. Hint: Use the relation between the greatest common divisor and the least common multiple. Then reuse the code for Euclid's algorithm for greatest common divisor.

  2. For any positive integer n, let F(n) be the number of primes less than or equal to n. Write a program which prompts for a positive integer and then prints the value of F(n).

    Remark : The prime number theorem (conjectured by Gauss, and proved by Hadamard and de la Vallee Poussin in 1896) states that F(n)/n * log(n) tends to 1 as n tends to infinity. You can use your solution to test it.

  3. Determine all solutions (accurate up to six decimal places) of the equation 4* cos(x) = a*x, where a = 0.4xxx is a decimal number (xxx represent the last three digits of your student id number). Use either bisection or Newton's method. Describe in detail the procedure you used to find the answer, enclose the programs and the final result.

E-mail your solutions to milicic@math.utah.edu. This assignment is due March 31th.