> Number Theory
Sometimes called "Euclid's lemma" in textbooks when appearing before a proof of the fundamental theorem of arithmetic
. It states that if p
is a prime number
, then either p|a
("|" means "divides").
- If p is a prime and p|an, then p|a.
- If a and c are relatively prime, then c|ab implies c|b.
Incidentally, Euclid's Second Theorem states that there are infinitely many primes
"Euclid's First Theorem" is sometimes referred as such according to MathWorld.com.
Many of these theorems appear in Euclid's Elements
, proposition 30
states Euclid's First Theorem.
, proposition 14
partially states the fundamental theorem of arithmetic
states Euclid's Second Theorem.
Thanks to Swap
for tipping me off about this.