prime factorization in a sentence

Examples

1. Both are written as exponentiation modulo a composite number, and both are related to the problem of prime factorization.
2. It is based on ideas such as divisibility and fundamental theorem states that each positive integer has a unique prime factorization.
3. The value of each variable is encoded as the exponent of a prime number in the prime factorization of the integer.
4. If these integers are further restricted to prime numbers, the process is called "'prime factorization " '.
5. Essentially we have an integer " i " which has a prime " p " in its prime factorization.
6. There is a version of unique prime factorization for the ideals of a Dedekind domain ( a type of ring important in number theory ).
7. As a result, there is no smallest positive integer with multiple prime factorizations, hence all positive integers greater than 1 factor uniquely into primes.
8. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of G�del numbering.
9. So, albeit there are many prime factorization algorithms to do this in practice for larger numbers, they all have to yield the same result.
10. A positive integer can be represented as a sum of two squares precisely if its prime factorization contains no odd powers of primes of the form.