Order of Element Modulo n Calculator
Discover the order of an element modulo n. This tool helps you find the smallest positive integer k such that ak ≡ 1 (mod n).
a
n
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The order of modulo is:
Visualization of ak mod n
| k | ak mod n |
|---|---|
What is the Order of an Element Modulo n?
In modular arithmetic, the order of an integer 'a' modulo 'n' is the smallest positive integer 'k' such that ak is congruent to 1 modulo 'n'. In simpler terms, it's the smallest power 'k' to which you must raise 'a' so that the remainder when ak is divided by 'n' is 1.
- Formula: ak ≡ 1 (mod n)
- Example: The order of 3 modulo 7 is 6, because 36 ≡ 1 (mod 7), and no smaller positive integer exponent works.
- Use Cases: Order of elements is a fundamental concept in number theory and has applications in cryptography, especially in algorithms like Diffie-Hellman key exchange.
Learn more about order of elements on resources like Wikipedia and Khan Academy.