Purchase Solution

Discrete Mathematics : Integer Algorithms, GCD, Solving Congruences and Diagonal Matrices

Not what you're looking for?

Ask Custom Question

4. Describe an algorithm that takes as input a list of n integers and produces as output the largest difference between consecutive integers in the list.

Integers
28. What is the greatest common divisors of these pairs of integers?
a) 22 * 33 * 55, 25 * 33 * 52
b) 2 * 3 * 5 * 7 * 11 * 13, 211 * 39 * 11 * 1714
c) 17, 1717
d) 22 * 7, 53 * 13
e) 0, 5
f) 2 * 3 * 5 * 7, 2 * 3 * 5 * 7

Number Theory
18. Find all solutions to the system of congruences.
x = 2(mod 3)
x = 1(mod 4)
x = 3(mod 5)

Matrices
14. The n x n matrix A = [aij] is called a diagonal matrix if aij = 0 when i ≠ j. Show that the product of two n x n diagonal matrices is again a diagonal matrix. Give a simple rule for determining this product.

For each topic, demonstrate a knowledge and capability by giving the following information:

1) Problem Solution: (solution for an even number problem) see below...

2) Personal Observation: (personal comment on the topic including advice to others on how to study and understand it).

Attachments
Purchase this Solution

Solution Summary

Integer Algorithms, GCD, Solving Congruences and Diagonal Matrices are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

4.)
do (i=1 to n) { read a[i]}
max_diff = 0.0
do (i=2 to n)
{ diff = |a[i] - a[i-1] |
if diff > max_diff then max_diff = diff }
Print max_diff

28.)
Take corresponding to each prime factor, highest common index (e.g., 2^3 and 2^5: GCD = 2^3)
a.)
2^2 * 3^3 * 5^5, 2^5 * 3^3 * 5^2
greatest common factors: 2^2 * 3^3 * 5^2 = 2700 --Answer (common indices of 2: 2, of 3: 3, of 5: 2)

b)2 * 3 * 5 * 7 * 11 * 13, 2^11 * 3^9 * 11 * ...

Solution provided by:
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.