Question

Problems 11.3, No. 14 (a) and (b) from page 237 of David M. Burton's "Elementary Number Theory" (7th Edition)

score 159 · Answer 1 · 2020-03-10 09:41:44

159

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Problems 11.3, No. 14 (a) and (b) from page 237 of David M. Burton's "Elementary Number Theory" (7th Edition)

Published on 10 Mar 2020 - 9:41

score 96 · Answer 2 · 2026-03-26 00:53:57

96

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If $p^k m^2$ is an odd perfect number with special prime $p$, then what is wrong about the following factor chain approach to proving $p \neq 5$?

Published on 26 Mar 2026 - 0:53

score 181 · Answer 3 · 2026-03-22 20:02:05

181

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Summing Odd Fractions to One, and Odd Perfect Numbers

Published on 22 Mar 2026 - 20:02

score 86 · Answer 4 · 2020-03-30 08:46:56

86

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On bounds for the deficiency of $m^2$, where $p^k m^2$ is an odd perfect number with special prime $p$

Published on 30 Mar 2020 - 8:46

score 1.1k · Answer 5 · 2026-02-23 03:40:24

1.1k

Views

Why did the Egyptians not represent $2/3$ as a sum of unit fractions in the Rhind papyrus?

Published on 23 Feb 2026 - 3:40

score 91 · Answer 6 · 2020-04-02 09:35:01

91

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On the least number of factors $\sigma(q^{e_q})$ to get the least multiple of $\operatorname{rad}(n)$, on assumption that $n$ is an odd perfect number

Published on 02 Apr 2020 - 9:35

score 43 · Answer 7 · 2026-03-25 14:26:57

43

Views

On solutions of $\varphi(n)=\frac{1}{2n}\sum_{1\leq d\mid n}\varphi(dn)$, where $\varphi(m)$ denotes the Euler's totient function

Published on 25 Mar 2026 - 14:26

score 82 · Answer 8 · 2020-04-04 11:44:42

82

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Is there a number $\mathscr{D}_2 \neq \mathscr{D} = {{3003}^2}\cdot{22021}$ satisfying a certain condition?

Published on 04 Apr 2020 - 11:44

score 87 · Answer 9 · 2020-04-06 04:04:47

87

Views

Show that if n is an even perfect number then n is not the sum of two squares.

Published on 06 Apr 2020 - 4:04

score 68 · Answer 10 · 2020-04-10 18:05:46

68

Views

Is the last digit of $2^{2^{n-1}(2^n-1)}-1$ always $5$ for $n >3$?

Published on 10 Apr 2020 - 18:05

score 339 · Answer 11 · 2020-04-14 19:57:53

339

Views

Attempt to get a characterization of even perfect numbers from an equation involving the Dedekind psi function

Published on 14 Apr 2020 - 19:57

score 139 · Answer 12 · 2020-04-15 10:22:15

139

Views

On odd perfect numbers and a GCD - Part II

Published on 15 Apr 2020 - 10:22

score 59 · Answer 13 · 2020-04-19 19:08:35

59

Views

Is $n=6$ the only integer satisfying phenomenal properties in number theory ? if yes then why?

Published on 19 Apr 2020 - 19:08

score 76 · Answer 14 · 2026-02-23 02:57:41

76

Views

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Published on 23 Feb 2026 - 2:57

score 40 · Answer 15 · 2020-04-23 01:17:35

40

Views

Assume an odd perfect number exists could be it written as $x^3+y^3+z^3$?

Published on 23 Apr 2020 - 1:17

List Question

Problems 11.3, No. 14 (a) and (b) from page 237 of David M. Burton's "Elementary Number Theory" (7th Edition)

If $p^k m^2$ is an odd perfect number with special prime $p$, then what is wrong about the following factor chain approach to proving $p \neq 5$?

Summing Odd Fractions to One, and Odd Perfect Numbers

On bounds for the deficiency of $m^2$, where $p^k m^2$ is an odd perfect number with special prime $p$

Why did the Egyptians not represent $2/3$ as a sum of unit fractions in the Rhind papyrus?

On the least number of factors $\sigma(q^{e_q})$ to get the least multiple of $\operatorname{rad}(n)$, on assumption that $n$ is an odd perfect number

On solutions of $\varphi(n)=\frac{1}{2n}\sum_{1\leq d\mid n}\varphi(dn)$, where $\varphi(m)$ denotes the Euler's totient function

Is there a number $\mathscr{D}_2 \neq \mathscr{D} = {{3003}^2}\cdot{22021}$ satisfying a certain condition?

Show that if n is an even perfect number then n is not the sum of two squares.

Is the last digit of $2^{2^{n-1}(2^n-1)}-1$ always $5$ for $n >3$?

Attempt to get a characterization of even perfect numbers from an equation involving the Dedekind psi function

On odd perfect numbers and a GCD - Part II

Is $n=6$ the only integer satisfying phenomenal properties in number theory ? if yes then why?

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Assume an odd perfect number exists could be it written as $x^3+y^3+z^3$?

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