Question

Can the existence of infinitely many even perfect numbers be settled by a diagonal argument?

score 55 · Answer 1 · 2015-12-08 17:08:27

55

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Can the existence of infinitely many even perfect numbers be settled by a diagonal argument?

Published on 08 Dec 2015 - 17:08

score 44 · Answer 2 · 2016-02-07 15:35:25

44

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If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

Published on 07 Feb 2016 - 15:35

score 46 · Answer 3 · 2016-02-18 23:29:30

46

Views

Why $\frac{2a+2b-4}{5b-4}<1$?

Published on 18 Feb 2016 - 23:29

score 75 · Answer 4 · 2016-02-25 14:34:21

75

Views

If $b$ is an odd composite number and $\dfrac{b^2 - 1}{\sigma(b^2) - b^2} = q$ is a prime number, what happens when $q = 2^{r + 1} - 1$?

Published on 25 Feb 2016 - 14:34

score 113 · Answer 5 · 2016-02-25 20:35:00

113

Views

Does the Descartes number $D = 198585576189$ have a friend?

Published on 25 Feb 2016 - 20:35

score 41 · Answer 6 · 2016-03-09 07:26:35

41

Views

Requesting for details of Grun's result on odd perfect numbers

Published on 09 Mar 2016 - 7:26

score 7.5k · Answer 7 · 2016-03-17 16:40:56

7.5k

Views

Could a square be a perfect number?

Published on 17 Mar 2016 - 16:40

score 138 · Answer 8 · 2016-03-24 04:36:37

138

Views

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

Published on 24 Mar 2016 - 4:36

score 222 · Answer 9 · 2016-03-31 00:07:22

222

Views

Proving this quotient is always even.

Published on 31 Mar 2016 - 0:07

score 134 · Answer 10 · 2016-03-31 12:02:38

134

Views

Odd Perfect Numbers attempt

Published on 31 Mar 2016 - 12:02

score 113 · Answer 11 · 2016-04-02 14:10:06

113

Views

Even perfect numbers and a relationship with polygonal numbers

Published on 02 Apr 2016 - 14:10

score 91 · Answer 12 · 2016-04-04 13:20:38

91

Views

Perfect numbers of the form $12m+1$ and $\sum_{d\mid n}\frac{1}{\phi(d)}$, where $\phi(m)$ is Euler's totient function

Published on 04 Apr 2016 - 13:20

score 77 · Answer 13 · 2016-04-04 17:51:30

77

Views

For which $r$ the expression $\sqrt{4s+ r^2}$ is an integer?

Published on 04 Apr 2016 - 17:51

score 67 · Answer 14 · 2016-04-05 09:12:42

67

Views

A cubic relationship for perfect numbers

Published on 05 Apr 2016 - 9:12

score 218 · Answer 15 · 2016-04-06 10:27:11

218

Views

On the Density of Deficient Odd Numbers and Abundant Integers

Published on 06 Apr 2016 - 10:27

List Question

Can the existence of infinitely many even perfect numbers be settled by a diagonal argument?

If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

Why $\frac{2a+2b-4}{5b-4}<1$?

If $b$ is an odd composite number and $\dfrac{b^2 - 1}{\sigma(b^2) - b^2} = q$ is a prime number, what happens when $q = 2^{r + 1} - 1$?

Does the Descartes number $D = 198585576189$ have a friend?

Requesting for details of Grun's result on odd perfect numbers

Could a square be a perfect number?

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

Proving this quotient is always even.

Odd Perfect Numbers attempt

Even perfect numbers and a relationship with polygonal numbers

Perfect numbers of the form $12m+1$ and $\sum_{d\mid n}\frac{1}{\phi(d)}$, where $\phi(m)$ is Euler's totient function

For which $r$ the expression $\sqrt{4s+ r^2}$ is an integer?

A cubic relationship for perfect numbers

On the Density of Deficient Odd Numbers and Abundant Integers

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