EECS 310 Mathematical Foundations of Computer Science
Department of Electrical Engineering and Computer Science
Northwestern University

Fall 2006

Problem Set #1

Due Time:

At the start of class on Friday, 10/6/2006.

Required Problems:

  1. (20 points) Give a formula for the following summation:

15 + 25 + 35 + ... + (n-1)5 + n5

  1. (20 points) Give a formula for the following summation:

13r0 + 23r1 + 33r2 + ... + (n-1)3r(n-2) + n3r(n-1)

  1. (20 points) Find two integers x and y such that 103x + 851 y = GCD(103, 851).
  1. (20 points) Find the number of integer solutions to the following equation:

x1 + x2 + x3 + x4 + x5 + x6 = 100,

where x1 > 1 , x2 ≥ 6, x3 ≥ -1, x4 = -7, x5 > 90, x6 > 3.

  1. (10 points) Problem 7 on page 18.
  1. (10 points) Problem 14 on Page 27.

Extra Credit Problems:

  1. (10 points) Problem 12 on Page 39.