Proof
The proof uses Euclid's lemma (Elements VII, 30): if a prime p divides the product of two natural numbers a and b, then p divides a or p divides b (or perhaps both). The article has proofs of the lemma.
Read more about this topic: Fundamental Theorem Of Arithmetic
Famous quotes containing the word proof:
“A short letter to a distant friend is, in my opinion, an insult like that of a slight bow or cursory salutation—a proof of unwillingness to do much, even where there is a necessity of doing something.”
—Samuel Johnson (1709–1784)
“If any doubt has arisen as to me, my country [Virginia] will have my political creed in the form of a “Declaration &c.” which I was lately directed to draw. This will give decisive proof that my own sentiment concurred with the vote they instructed us to give.”
—Thomas Jefferson (1743–1826)
“War is a beastly business, it is true, but one proof we are human is our ability to learn, even from it, how better to exist.”
—M.F.K. Fisher (1908–1992)