Question

numbers representable as sums of perfect powers

score 295 · Answer 1 · 2017-11-29 20:49:23

295

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numbers representable as sums of perfect powers

Published on 29 Nov 2017 - 20:49

score 85 · Answer 2 · 2017-12-06 15:50:09

85

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Smallest positive integer $n$ such that $2^{1980}\cdot3^{384}\cdot5^{1694}\cdot7^{343}\cdot n$ is a $k$-th power for some $k\ge2$.

Published on 06 Dec 2017 - 15:50

score 51 · Answer 3 · 2017-12-08 03:12:16

51

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Power-of-two integer roundup maths algorithms

Published on 08 Dec 2017 - 3:12

score 300 · Answer 4 · 2017-12-15 17:24:10

300

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Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?

Published on 15 Dec 2017 - 17:24

score 101 · Answer 5 · 2017-12-26 12:09:06

101

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$ X^6 + Y^6 + Z^6 = A^6 + B^6 + C^6 = I^6 + J^6 + K^6 = T $

Published on 26 Dec 2017 - 12:09

score 9.7k · Answer 6 · 2010-11-23 20:03:55

9.7k

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$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$

Published on 23 Nov 2010 - 20:03

score 3.8k · Answer 7 · 2012-12-27 17:53:24

3.8k

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Product of three consecutive positive integers is never a perfect power

Published on 27 Dec 2012 - 17:53

score 1.9k · Answer 8 · 2013-02-08 13:57:05

1.9k

Views

Given an integer, how can I detect the nearest integer perfect power efficiently?

Published on 08 Feb 2013 - 13:57

score 143 · Answer 9 · 2020-08-07 21:29:35

143

Views

Can a multiperfect number be a perfect power?

Published on 07 Aug 2020 - 21:29

score 73 · Answer 10 · 2020-08-22 08:12:55

73

Views

If there is a way to express an integer as a sum of three non-zero cubes, then there are infinitely many ways

Published on 22 Aug 2020 - 8:12

score 317 · Answer 11 · 2020-08-22 13:19:42

317

Views

How to check if a number can be represented as the sum of two consecutive perfect cubes.

Published on 22 Aug 2020 - 13:19

score 265 · Answer 12 · 2026-02-23 07:40:28

265

Views

Power values of polynomial

Published on 23 Feb 2026 - 7:40

score 76 · Answer 13 · 2026-03-25 09:31:54

76

Views

Extending Given Digits to make Perfect Powers

Published on 25 Mar 2026 - 9:31

score 60 · Answer 14 · 2020-10-04 12:25:07

60

Views

Infinitely many consecutive powers with no consecutive equal digits?

Published on 04 Oct 2020 - 12:25

score 124 · Answer 15 · 2020-10-23 11:23:37

124

Views

Has this family of Diophantine equations ever been studied?

Published on 23 Oct 2020 - 11:23

List Question

numbers representable as sums of perfect powers

Smallest positive integer $n$ such that $2^{1980}\cdot3^{384}\cdot5^{1694}\cdot7^{343}\cdot n$ is a $k$-th power for some $k\ge2$.

Power-of-two integer roundup maths algorithms

Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?

$ X^6 + Y^6 + Z^6 = A^6 + B^6 + C^6 = I^6 + J^6 + K^6 = T $

$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$

Product of three consecutive positive integers is never a perfect power

Given an integer, how can I detect the nearest integer perfect power efficiently?

Can a multiperfect number be a perfect power?

If there is a way to express an integer as a sum of three non-zero cubes, then there are infinitely many ways

How to check if a number can be represented as the sum of two consecutive perfect cubes.

Power values of polynomial

Extending Given Digits to make Perfect Powers

Infinitely many consecutive powers with no consecutive equal digits?

Has this family of Diophantine equations ever been studied?

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