prime factorization, and differs from every The former case is also impossible, as, if is a divisor of it must be also a divisor of which is impossible as and are distinct primes.

Therefore, there cannot exist a smallest integer with more than a single distinct prime factorization. Every positive integer must either be a prime number itself, which would factor uniquely, or a composite that also factors uniquely into primes, or in the case of the integer , not factor into any prime.

Generalizations

The first generalization

1.Previous
3.Next