List questions from prime-factorization

Published on 02 Jul 2017 - 4:57

54

Views

For which $n$ is the number of such pairs $x,y$ with $\operatorname{lcm}(x,y)=n!$,$\gcd{(x,y)}=1998$

Published on 24 Feb 2026 - 8:35

110

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What is the "purely elementary reasoning" that the number of distinct prime factors of $n$ grows like $\frac{\log n}{\log \log n}$?

Published on 06 Jul 2017 - 13:41

9k

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What can be the maximum and minimum number of prime factors?

Published on 07 Jul 2017 - 7:34

338

Views

When Does $\sigma(q^k)$ Have a Prime Factor Greater Than $q$

Published on 08 Jul 2017 - 2:04

1.3k

Views

factorization algorithm in PARI/GP

Published on 11 Jul 2017 - 9:13

625

Views

Lower bounds for integer factorization

Published on 11 Jul 2017 - 10:58

243

Views

Semiprimes with three (and more) numbers

Published on 23 Feb 2026 - 8:23

67

Views

Is $(2^a - 3^b)$ mutually prime with $(2^a - ((2^a)^{-1} \mod 3^b ) - ((3^b)^{-1} \mod 2^a))$?

Published on 12 Jul 2017 - 3:14

643

Views

Primary Decomposition

Published on 12 Jul 2017 - 17:09

195

Views

Proving a number is a factor of a in (a mod N)

Published on 13 Jul 2017 - 3:24

117

Views

Prime factorisation of ideals

Published on 17 Jul 2017 - 12:00

343

Views

Proof using prime factorization and fundamental theorem of arithmetic

Published on 18 Jul 2017 - 22:30

299

Views

Estimates for Sum of Prime Factors and Number of Prime Factors

Published on 30 Mar 2026 - 11:59

137

Views

Justifying the representation of a monic polynomial over a UFD

Published on 30 Mar 2026 - 0:19

List Question

polynomial ring prime element

For which $n$ is the number of such pairs $x,y$ with $\operatorname{lcm}(x,y)=n!$,$\gcd{(x,y)}=1998$

What is the "purely elementary reasoning" that the number of distinct prime factors of $n$ grows like $\frac{\log n}{\log \log n}$?

What can be the maximum and minimum number of prime factors?

When Does $\sigma(q^k)$ Have a Prime Factor Greater Than $q$

factorization algorithm in PARI/GP

Lower bounds for integer factorization

Semiprimes with three (and more) numbers

Is $(2^a - 3^b)$ mutually prime with $(2^a - ((2^a)^{-1} \mod 3^b ) - ((3^b)^{-1} \mod 2^a))$?

Primary Decomposition

Proving a number is a factor of a in (a mod N)

Prime factorisation of ideals

Proof using prime factorization and fundamental theorem of arithmetic

Estimates for Sum of Prime Factors and Number of Prime Factors

Justifying the representation of a monic polynomial over a UFD

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