Fundamental theorem of arithmetic (thing) by neil

Every nonzero non-unit (not 1 or -1) integer has a unique prime factorisation, up to permutation of the factors and replacement of some factors by their associates.

An integral domain for which the above holds (substituting `irreducible' for `prime'; I think it matters) is called a `unique factorisation domain'. In all UFDs, an element is prime iff it is irreducible.

Fundamental theorem of algebra	Fundamental theorem of calculus	Ten largest known primes	Well Ordering Theorem
n nth complex roots of unity	unique factorization domain	Gaussian integer	1 is not prime
Gödel's theorem	Carol Vorderman	Euclid's First Theorem	WLOG
The 7-Eleven problem	Prime decomposition	Goldbach's conjecture	Is it possible to pack two transcendental numbers?
How to smoke marijuana	proof that the sum of the reciprocals of the primes diverges	Eratosthenes' Sieve	Automorphism
IFF	prime	Lexical decomposition