Science Fair Project Encyclopedia
Euclid's lemma
Euclid's lemma is a generalisation of Proposition 30 of Book VII of Euclid's Elements. The lemma states that
- If a positive integer divides the product of two other positive integers, and the first and second integers are coprime, then the first integer divides the third integer.
This can be written in notation:
- If a|bc and gcd(a,b)=1 then a|c.
Proposition 30 states:
- If a prime number divides the product of two positive integers, then the prime number divides at least one of the positive integers.
- If p|bc then p|b or p|c.
See also
Last updated: 05-28-2005 04:06:11
11-30-2008 18:11:33
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details