Difference between revisions of "Greatest common divisor"
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===Co-prime=== | ===Co-prime=== | ||
If for {{M|a,b\in\mathbb{N}_+}} we have {{M|1=\text{gcd}(a,b)=1}} then {{M|a}} and {{M|b}} are said to be ''co-prime''<ref name="Crypt"/> | If for {{M|a,b\in\mathbb{N}_+}} we have {{M|1=\text{gcd}(a,b)=1}} then {{M|a}} and {{M|b}} are said to be ''co-prime''<ref name="Crypt"/> | ||
| − | + | ====Coprime==== | |
| + | Coprime is used by some authors, co-prime by others. I prefer the hyphenated form because to be ''co-something'' implies more than one thing is involved. You cannot have "a coprime number" but you can have a pair of co-prime numbers. | ||
==See next== | ==See next== | ||
* [[Euclidean algorithm]] | * [[Euclidean algorithm]] | ||
Revision as of 08:28, 21 May 2015
Note: requires knowledge of what it means for a number to be a divisor of another.
Contents
[hide]Definition
Given two positive integers, a,b∈N+, the greatest common divisor of a and b[1] is the greatest positive integer, d, that divides both a and b. We write:
- d=gcd(a,b)
Terminology
Co-prime
If for a,b∈N+ we have gcd(a,b)=1 then a and b are said to be co-prime[1]
Coprime
Coprime is used by some authors, co-prime by others. I prefer the hyphenated form because to be co-something implies more than one thing is involved. You cannot have "a coprime number" but you can have a pair of co-prime numbers.
See next
See also
References
- ↑ Jump up to: 1.0 1.1 The mathematics of ciphers, Number theory and RSA cryptography - S. C. Coutinho
