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

Not what you're looking for?

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).

##### 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 * ...

###### 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.