Modulo arthmetic solve for x^N .

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In summary, we are trying to solve the problem x^N = a mod b for x, where b, N, and a are not prime numbers. There is no generic solution for this problem, but providing the actual numbers would be helpful. One approach is to factor b, use Fermat's little theorem, and then use the Chinese remainder theorem to combine the results.
  • #1
shadowhywind
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Modulo arthmetic solve for x^N...

Hay all, I am stuck on a problem, and its driving me crazy. I have a problem, xN = a mod b. Where I have to solve for x. My first thought was use to Fermat's little theorem(if I have the name correct), however my b is not a prime, (neither is 'N' or 'a' for that fact). I can give the exact problem with numbers if needed, but thought it would be slightly easier with variables instead. Any tips on how I could start to solve this would be great. Any questions please ask.
 
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  • #2


I believe there is no generic solution to this problem.
 
  • #3


Giving the actual numbers would probably be best for this one.
 
  • #4


Google nth power residue for lots of results (and references to specific number theory texts) regarding your question.

Petek
 
  • #5


Chinese remainder theorem.
 
  • #6


Hurkyl said:
Chinese remainder theorem.

Yes. Factor b, use Fermat, then CRT the results together.
 

Related to Modulo arthmetic solve for x^N .

1. What is modulo arithmetic?

Modulo arithmetic is a mathematical operation that involves finding the remainder when a number is divided by another number. It is often used in cryptography and computing to create unique numbers or to perform calculations on large numbers.

2. How is modulo arithmetic used to solve for x^N?

To solve for x^N using modulo arithmetic, we first take the base number (x) and raise it to the power of the exponent (N). Then, we divide the result by the modulo (usually denoted by the symbol %) to find the remainder. This remainder is the solution for x^N.

3. What are some real-life applications of modulo arithmetic?

Modulo arithmetic has various real-life applications, such as generating unique identification numbers, calculating checksums in data transmission, and creating secure encryption algorithms.

4. How does modulo arithmetic differ from regular arithmetic?

The main difference between modulo arithmetic and regular arithmetic is that in modulo arithmetic, we only consider the remainder when dividing two numbers. In regular arithmetic, we take into account the quotient as well.

5. Can modulo arithmetic be performed on negative numbers?

Yes, modulo arithmetic can be performed on negative numbers. The remainder will always be a positive number, so if the result of the operation is negative, we can simply add the modulo to it to get a positive remainder.

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