Understanding x=pmodn: An Integer Modular Arithmetic Primer

In summary, modular arithmetic is a branch of mathematics that deals with operations on integers within a specific range, denoted as "mod n". The expression x=pmodn represents equivalence between two integers with a difference that is a multiple of n, and is commonly used in cryptography and number theory. To calculate x=pmodn, the remainder of x divided by n is compared to p. Modular arithmetic has many applications in fields such as cryptography and computer science, and an example of x=pmodn would be 14=2mod6, showing that 14 and 2 are equivalent when considering the modulus of 6.
  • #1
Ed Quanta
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What does x=pmodn mean where x,p,are integers and n is a natural number?
 
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  • #3
Cookiemonster's statement is true as long as you assume that p< n, which is the most common use. More generally, "x= p, mod n" (actually "x congruent to p mod n" with the congruence sign having 3 lines instead of only two like "="), means that x-p is exactly divisible by n.
 

1. What is modular arithmetic?

Modular arithmetic is a branch of mathematics that deals with operations on integers, where the result of the operation is always within a specific range, called the modulus. This range is usually denoted by "mod n", where n is a positive integer.

2. What is the purpose of x=pmodn?

The expression x=pmodn is a shorthand notation for "x is congruent to p modulo n". It is used to represent the concept of equivalence between two integers, where the difference between them is a multiple of n. This is useful in various applications, such as cryptography and number theory.

3. How is x=pmodn calculated?

To calculate x=pmodn, you first need to determine the remainder when x is divided by n. This remainder is then compared to p. If they are equal, then x is congruent to p modulo n. If they are not equal, then x is not congruent to p modulo n.

4. What are some common applications of modular arithmetic?

Modular arithmetic has many applications in various fields, including cryptography, computer science, and number theory. It is used in encryption algorithms, error correction codes, and in the study of prime numbers.

5. Can you provide an example of x=pmodn?

Sure, let's say we have the expression 14=2mod6. This means that 14 is congruent to 2 modulo 6, because when we divide 14 by 6, the remainder is 2. Another way to write this would be 14 mod 6 = 2, which shows that 14 and 2 are equivalent when considering the modulus of 6.

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