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Results tagged with factorization
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user 37555
For questions about factorization, the decomposition of mathematical objects (e.g. natural numbers, polynomials) into products of smaller objects (e.g. primes, lower degree polynomials).
3
votes
Is there a "small $\omega$" number theorem?
The integers in the interval $[n, n+D]$ have level of distribution close to $D$, hence you can apply a lower bound sieve (e.g. http://www.math.uiuc.edu/~ford/sieve_notes_intro_brun_hooley.pdf, Theorem …
2
votes
How much space between these smooth numbers?
The local behaviour of smooth numbers is extremely difficult.
If $p\equiv 3\pmod{4}$ is prime, and $n$ is the least quadratic non-residue modulo $p$, then all integers with prime factors $<n$ are squ …
1
vote
Is it possible to show that :for $n \geq 1:\sigma(n!-1) $ never be prime and why $\sigma(n!-...
However, proving this statement is either easy, because some factorization or congruence argument works, or almost impossible. …