Solve Modular Math Problem: A,B→C

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In summary, to find C = f(A, B) with the given conditions, use Euclid's Algorithm on B and 2**A. Use the extended Euclidean algorithm to find two numbers, u and v, such that -u * m + gcd(m, n) = v * n. This method works because B is odd and 2**A is a power of two, making them coprime.
  • #1
Gokul43201
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Given, A>0 and odd B>0, find C = f(A,B), satisfying :

1 + BC == 0 (mod 2^A)
 
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  • #2
Euclid's Algorithm on B and 2**A will do it. sorry, my six key is buggered so i can't do powers in pseudotex.
 
  • #3
matt,

I'm not sure I follow. You are talking about the GCD algorithm, right ?

I don't see how this works. Can you show me how, on an example, say 2^A = 64, B = 15 ?
 
  • #4
Recall that the extended Euclidean algorithm will give you two numbers, u and v, such that u * m + v * n = gcd(m, n)...
 
  • #5
Yes, I've used it to solve linear diophantine eqns...but don't see how it can be used here.
 
  • #6
B is odd, 2**A is a power of two, they are coprime.
 
  • #7
Maybe it would help if I rewrite it as

(-u) * m + gcd(m, n) = v * n

?
 
  • #8
Thanks,

I never cease to amaze myself !
 

FAQ: Solve Modular Math Problem: A,B→C

What is modular math?

Modular math, also known as modular arithmetic, is a type of mathematics that deals with numbers and operations on numbers within a specific set or "module". It is often used in computer science and cryptography, and has various real-world applications.

How do you solve a modular math problem?

To solve a modular math problem, you first need to understand the rules of modular arithmetic. This includes the concept of modular congruence and how to perform operations such as addition, subtraction, multiplication, and division within a given module. You can then use these rules to solve the problem by following the standard order of operations.

What is the notation used for modular math?

The notation used for modular math is typically "a ≡ b (mod n)", where "a" and "b" are integers and "n" is the modulus. This notation represents the congruence of "a" and "b" in the given module "n".

Can you provide an example of solving a modular math problem?

Sure, for example, if we have the problem A,B → C where A = 7, B = 4, and the modulus is 5, we can solve it as follows:

A ≡ 7 (mod 5) and B ≡ 4 (mod 5)

7 + 4 ≡ C (mod 5)

11 ≡ C (mod 5)

C = 1

Therefore, the solution to A,B → C is C = 1.

What are the practical applications of modular math?

Modular math is used in various fields such as computer science, cryptography, and coding theory. It is also commonly used in calculating time and dates, designing calendars, and creating musical scales. Additionally, modular math has applications in solving real-world problems such as optimizing resources and scheduling tasks.

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