User Jose Arnaldo Bebita

5 votes

Algebraic Attacks on the Odd Perfect Number Problem

answered Oct 28, 2010 at 5:35

5 votes

Cyclotomic polynomials in combinatorics

answered Oct 5, 2013 at 16:13

5 votes

Not especially famous, long-open problems which higher mathematics beginners can understand

answered Oct 26, 2015 at 17:39

4 votes

Computer science for mathematicians

answered Jan 6, 2011 at 22:01

4 votes

"Modern" proof for the Baker-Campbell-Hausdorff formula

answered Jun 10, 2012 at 18:11

3 votes

Generalized quasi-perfect numbers

answered May 29, 2016 at 1:47

3 votes

Has it been proved that odd perfect numbers cannot be triangular?

answered Jan 24, 2017 at 18:26

2 votes

A conjecture regarding odd perfect numbers

answered Sep 8, 2019 at 1:10

2 votes

Resources where I can find open problems in number theory along with their level of difficulty

answered May 12, 2022 at 2:28

2 votes

How do we recognize an integer inside the rationals?

answered Aug 10, 2013 at 23:58

2 votes

Elementary + short + useful

answered Dec 3, 2011 at 19:37

2 votes

References for Yang-Mills Theory

answered Apr 28, 2016 at 7:40

1 vote

Accepted

Short papers in applied probability

answered Jan 6, 2016 at 15:47

1 vote

Can a number be factored quickly, given the sum of its prime factors?

answered Mar 7, 2011 at 2:06

1 vote

Accepted

Existence of Solutions to an Equation Involving the Sum-of-Divisors Function [Reference Request]

answered Mar 3, 2011 at 5:14

1 vote

On odd perfect numbers and a GCD

answered Mar 2, 2019 at 13:24

1 vote

Accepted

Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

answered Dec 23, 2021 at 2:58

1 vote

Accepted

What can be said about $\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$?

answered Nov 5, 2023 at 4:40

1 vote

On odd perfect numbers and a GCD

answered Apr 15, 2020 at 6:41

1 vote

Can $k$ be arbitrarily large in the following equations?

answered Jun 9, 2017 at 7:25

1 vote

Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd perfect number?

answered Jun 1, 2016 at 14:33

0 votes

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

answered Feb 4, 2021 at 3:21

0 votes

Accepted

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

answered Sep 16, 2021 at 4:42

0 votes

Accepted

On odd perfect numbers and a GCD - Part III

answered Jul 26, 2022 at 23:46

0 votes

Accepted

If $p^k m^2$ is an odd perfect number with special prime $p$, then under what other conditions on $\sigma(p^k)/2$ does $k=1$ follow?

answered Jan 5, 2023 at 9:46

0 votes

Accepted

Given that $H = \frac{n^2}{\sigma(q^k)/2} = G \times J^2$, where $q^k n^2$ is an odd perfect number, then what is the value of $\gcd(G, J)$?

answered Jan 8, 2023 at 13:40

0 votes

A conjecture regarding odd perfect numbers

answered May 13, 2023 at 21:58

0 votes

A conjecture regarding odd perfect numbers

answered May 18, 2023 at 15:34

0 votes

Accepted

Reference Request - Sharp Estimates for a Logarithmic Sum

answered Mar 3, 2011 at 9:52

0 votes

Accepted

Perfect Numbers - On Mersenne and Euler Primes

answered Mar 12, 2011 at 12:44

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37 Answers

Algebraic Attacks on the Odd Perfect Number Problem

Cyclotomic polynomials in combinatorics

Not especially famous, long-open problems which higher mathematics beginners can understand

Computer science for mathematicians

"Modern" proof for the Baker-Campbell-Hausdorff formula

Generalized quasi-perfect numbers

Has it been proved that odd perfect numbers cannot be triangular?

A conjecture regarding odd perfect numbers

Resources where I can find open problems in number theory along with their level of difficulty

How do we recognize an integer inside the rationals?

Elementary + short + useful

References for Yang-Mills Theory

Short papers in applied probability

Can a number be factored quickly, given the sum of its prime factors?

Existence of Solutions to an Equation Involving the Sum-of-Divisors Function [Reference Request]

On odd perfect numbers and a GCD

Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

What can be said about $\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$?

On odd perfect numbers and a GCD

Can $k$ be arbitrarily large in the following equations?

Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd perfect number?

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

On odd perfect numbers and a GCD - Part III

If $p^k m^2$ is an odd perfect number with special prime $p$, then under what other conditions on $\sigma(p^k)/2$ does $k=1$ follow?

Given that $H = \frac{n^2}{\sigma(q^k)/2} = G \times J^2$, where $q^k n^2$ is an odd perfect number, then what is the value of $\gcd(G, J)$?

A conjecture regarding odd perfect numbers

A conjecture regarding odd perfect numbers

Reference Request - Sharp Estimates for a Logarithmic Sum

Perfect Numbers - On Mersenne and Euler Primes