Find a: Solve Discrete Math Problem with a & x Intergers

In summary, discrete math is a branch of mathematics that deals with countable or finite mathematical structures. It is used to solve problems involving discrete objects such as integers, sets, graphs, and logic. Integers play a crucial role in solving these problems, and techniques such as algebraic manipulation and combinatorics are used to find solutions. Discrete math has applications in various fields, including computer science, cryptography, and operations research.
  • #1
boiseneon
2
0
ok the problem is

Given that a and x are intergers, a>1, a|(11x+3), a|(55x+52), find a.

I am not sure how to even start this one to find a...any help please :cry:
 
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  • #2
There are integers p, q such that

11x + 3 = pa,
55x + 52 = qa.

Try eliminating x...
 
  • #3
ok how do I eliminate x??
 
  • #4
I am not at all familiar with number theory but I think got the answer:
First of all we have a>1>0 and x>0

11x+3=pa<=>55x+15=5pa (1)
55x+52=qa (2)

(2)-(1)=>37=(q-5p)a
q,p are natural numbers
So a|37 and 37 is a prime=> ...
 

Related to Find a: Solve Discrete Math Problem with a & x Intergers

1. What is discrete math?

Discrete math is a branch of mathematics that deals with mathematical structures that are countable or finite, such as integers, graphs, and sets. It is used to study and solve problems that involve discrete objects rather than continuous ones.

2. What is a discrete math problem?

A discrete math problem is a problem that can be solved using discrete mathematical concepts and tools. These problems typically involve integers, sets, graphs, logic, and combinatorics.

3. What is the role of integers in solving discrete math problems?

Integers play a crucial role in solving discrete math problems because they are used to represent discrete quantities or objects. They are also used in various mathematical operations such as addition, subtraction, and multiplication, which are essential in solving discrete math problems.

4. How do you solve a discrete math problem with integers and variables?

To solve a discrete math problem with integers and variables, you first need to define the problem and identify the variables involved. Then, you can use various techniques such as algebraic manipulation, logical reasoning, and combinatorics to find the solution. It is important to keep track of the constraints and assumptions while solving the problem.

5. What are some applications of discrete math?

Discrete math has various applications in computer science, cryptography, game theory, operations research, and other fields. It is used to solve problems related to networks, data structures, algorithms, and decision-making. It also has practical applications in business, finance, and engineering.

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