Understanding x=pmodn: An Integer Modular Arithmetic Primer

  • Context: High School 
  • Thread starter Thread starter Ed Quanta
  • Start date Start date
  • Tags Tags
    Arithmetic Integer
Click For Summary
SUMMARY

The expression x = p mod n defines a relationship in integer modular arithmetic where x is an integer that, when divided by the natural number n, leaves a remainder of p. This relationship holds true under the condition that p is less than n, which is the standard application. More generally, the notation "x ≡ p (mod n)" indicates that the difference x - p is divisible by n, reinforcing the concept of congruence in modular arithmetic.

PREREQUISITES
  • Understanding of integer modular arithmetic
  • Familiarity with congruence notation
  • Basic knowledge of divisibility rules
  • Awareness of natural numbers
NEXT STEPS
  • Research the properties of modular arithmetic
  • Learn about applications of congruences in number theory
  • Explore the use of modular arithmetic in cryptography
  • Study integer division and remainders in programming languages
USEFUL FOR

Mathematicians, computer scientists, and anyone interested in number theory or cryptographic applications will benefit from this discussion.

Ed Quanta
Messages
296
Reaction score
0
What does x=pmodn mean where x,p,are integers and n is a natural number?
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
  • · Replies 48 ·
2
Replies
48
Views
7K
Undergrad Congruence vs equality in mod arithmetic
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Modular arithmetic question about functions
  • · Replies 2 ·
Replies
2
Views
3K
High School Probability that 2 distinct integers are divisible by the same number
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Consecutive integers such that the prime divisors of each is less or equal to 3
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Sequence of integers and arithmetic progressions
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Fundamental Theorem of Arithmetic - Bhattacharya et al
  • · Replies 5 ·
Replies
5
Views
4K
MHB Fundamental Theorem of Arithmetic - Bhattacharya et al - Ch. 2, Section 1
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Meaning of terms in a direct sum decomposition of an algebra
  • · Replies 8 ·
Replies
8
Views
3K