Question

For which natural numbers $n ≥ 999$ is the number $N = \sqrt{n-999}+\sqrt{n+1000}$ natural?

score 64 · Answer 1 · 2023-10-25 14:07:55

64

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For which natural numbers $n ≥ 999$ is the number $N = \sqrt{n-999}+\sqrt{n+1000}$ natural?

Published on 25 Oct 2023 - 14:07

score 47 · Answer 2 · 2023-11-26 16:23:44

47

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Is there any square harmonic divisor number greater than $1$?

Published on 26 Nov 2023 - 16:23

score 94 · Answer 3 · 2026-02-23 05:10:53

94

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Can a Odd Perfect Number be a Carmichael Number?

Published on 23 Feb 2026 - 5:10

score 60 · Answer 4 · 2024-03-09 07:48:48

60

Views

Pattern of perfect numbers - why?

Published on 09 Mar 2024 - 7:48

score 44 · Answer 5 · 2024-03-13 08:12:45

44

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Why is this inequality in Brent and Cohens paper on odd perfect numbers true?

Published on 13 Mar 2024 - 8:12

score 46 · Answer 6 · 2024-03-14 11:24:05

46

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patterns in the abundancy index of integers

Published on 14 Mar 2024 - 11:24

score 4k · Answer 7 · 2015-01-25 04:03:32

4k

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Can the cube of every perfect number be written as the sum of three cubes?

Published on 25 Jan 2015 - 4:03

score 1.4k · Answer 8 · 2015-01-28 02:04:38

1.4k

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Prove that any power of a prime is not a perfect number

Published on 28 Jan 2015 - 2:04

score 63 · Answer 9 · 2026-03-26 01:07:58

63

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<Reference Request> Research done on whether the Euler prime can be the largest factor of an odd perfect number

Published on 26 Mar 2026 - 1:07

score 1.3k · Answer 10 · 2015-02-13 21:35:41

1.3k

Views

Product Perfect Numbers (Number Theory)

Published on 13 Feb 2015 - 21:35

score 1k · Answer 11 · 2015-02-15 02:03:06

1k

Views

Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.

Published on 15 Feb 2015 - 2:03

score 197 · Answer 12 · 2015-02-23 15:54:14

197

Views

Can an odd perfect number be divisible by $119$?

Published on 23 Feb 2015 - 15:54

score 128 · Answer 13 · 2015-03-08 03:32:56

128

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Databases for perfect numbers

Published on 08 Mar 2015 - 3:32

score 469 · Answer 14 · 2015-03-12 08:20:40

469

Views

Mersenne primes and superperfect numbers

Published on 12 Mar 2015 - 8:20

score 101 · Answer 15 · 2015-03-12 10:37:22

101

Views

A question related to the sum-of-divisors function

Published on 12 Mar 2015 - 10:37

List Question

For which natural numbers $n ≥ 999$ is the number $N = \sqrt{n-999}+\sqrt{n+1000}$ natural?

Is there any square harmonic divisor number greater than $1$?

Can a Odd Perfect Number be a Carmichael Number?

Pattern of perfect numbers - why?

Why is this inequality in Brent and Cohens paper on odd perfect numbers true?

patterns in the abundancy index of integers

Can the cube of every perfect number be written as the sum of three cubes?

Prove that any power of a prime is not a perfect number

<Reference Request> Research done on whether the Euler prime can be the largest factor of an odd perfect number

Product Perfect Numbers (Number Theory)

Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.

Can an odd perfect number be divisible by $119$?

Databases for perfect numbers

Mersenne primes and superperfect numbers

A question related to the sum-of-divisors function

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