List questions from perfect-powers

Published on 10 May 2026 - 9:56

94

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Can $2^s+3^s+\cdots +q^s$ , $q$ odd prime , $s\ge 2$ be a perfect power?

Published on 15 Apr 2026 - 2:25

238

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Conversion of arbitrary based numbers to different arbitrary base without division.

Published on 17 Apr 2026 - 2:39

167

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Can a prime have arbitary many representations as a sum of two perfect powers?

Published on 09 Apr 2026 - 13:03

72

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Can I complete the euclidean case without elliptic-curve-theory?

Published on 17 Apr 2026 - 15:51

990

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$p^2-p+1$ is a perfect cube of a prime

Published on 13 Apr 2026 - 14:27

190

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Is $2^9$ the only power of two that is the sum of two odd perfect powers?

Published on 11 Apr 2026 - 12:49

75

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Does concatenating the perfect powers ever lead to a prime?

Published on 08 Apr 2026 - 22:04

81

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The construction of a number with given digits

Published on 12 Apr 2026 - 6:28

192

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$2^W = (2a_1+1)^2 \cdot 2^{M_1}-a_1$ - is there a nontrivial diophantine solution in $M_1,a_1$ given possible?

Published on 16 Apr 2026 - 1:05

131

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Are there infinite many pairs of primes $(p/q)$ such that $p^3+q^3$ is a perfect square?

Published on 16 Apr 2026 - 5:32

168

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What's equal this:${\frac 12 ^ \frac 13} ^{\cdots \frac1n}$?

Published on 16 Apr 2026 - 14:47

182

Views

Prove that if $\Sigma_{i=1}^{n}(a_i)\le2^{n-4}$ then $a_2!a_3!\dots a_n!+1$ is not a power of $a_1$

Published on 15 Apr 2026 - 14:11

49

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Solving $x=2^y\cdot z$

Published on 16 Apr 2026 - 17:30

76

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finding perfect power factors of an integer

Published on 09 Apr 2026 - 9:25

List Question

Why $9k \pm 4$ can't be written as sum of four cubes

Can $2^s+3^s+\cdots +q^s$ , $q$ odd prime , $s\ge 2$ be a perfect power?

Conversion of arbitrary based numbers to different arbitrary base without division.

Can a prime have arbitary many representations as a sum of two perfect powers?

Can I complete the euclidean case without elliptic-curve-theory?

$p^2-p+1$ is a perfect cube of a prime

Is $2^9$ the only power of two that is the sum of two odd perfect powers?

Does concatenating the perfect powers ever lead to a prime?

The construction of a number with given digits

$2^W = (2a_1+1)^2 \cdot 2^{M_1}-a_1$ - is there a nontrivial diophantine solution in $M_1,a_1$ given possible?

Are there infinite many pairs of primes $(p/q)$ such that $p^3+q^3$ is a perfect square?

What's equal this:${\frac 12 ^ \frac 13} ^{\cdots \frac1n}$?

Prove that if $\Sigma_{i=1}^{n}(a_i)\le2^{n-4}$ then $a_2!a_3!\dots a_n!+1$ is not a power of $a_1$

Solving $x=2^y\cdot z$

finding perfect power factors of an integer

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