Sentence examples for factorization of numbers from inspiring English sources

Bézout's identity is essential to many applications of Euclid's algorithm, such as demonstrating the unique factorization of numbers into prime factors.

Most of the quantum algorithms have been implemented in NMR as Shor's algorithm [2] for the factorization of numbers.

Another example is the physical simulation of the factorization of numbers into primes that uses only polynomial resources in time and space, but requires an exponentially increasing precision.

The unique factorization of numbers into primes has many applications in mathematical proofs, as shown below.

Lamé's approach required the unique factorization of numbers of the form x + ωy, where x and y are integers, and ω = e2iπ/n is an nth root of 1, that is, ωn = 1.

These rely upon the factorization of gigantic numbers into primes a factorization that the code's user knows and the potential code-breaker does not.

The security of Rabin's scheme is based on the factorization of large numbers; thus, it is comparable to that of RSA too.

Quantum computation provides one possible way forward, since it has been shown theoretically that such devices can substantially speed up the solution of problems such as factorization of large numbers and database search and allow for the simulation of complex many-particle quantum systems.

Much remains unknown about the factorization of the numbers in the Sylvester's sequence.

Find the prime factorization of both numbers.

Find the prime factorization of the numbers, and list them out as shown.