pod
Indicates congruence modulo a number in number theory and abstract algebra, showing when two values have the same remainder upon division.
Overview
Serves as a specialized notation in mathematical contexts where modular arithmetic and number-theoretic relationships need to be expressed clearly.
- Common in cryptography and computer science for expressing modular relationships
- Used in abstract algebra for discussing equivalence classes and quotient rings
- Particularly useful when working with cyclic groups and periodic behaviors
- Often appears in proofs and theorems related to divisibility and number properties
Examples
Expressing a polynomial congruence relation modulo a prime number.
x^2 + 2x + 1 \pod{5}Showing equivalence of quadratic residues.
x^2 \pod{p}Representing a system of linear congruences in number theory.
3x + 2y \pod{7}