List questions from perfect-powers

Published on 27 Oct 2020 - 2:27

53

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Perfect powers in Horadam sequence

Published on 31 Oct 2020 - 10:10

148

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Solving $\tau^4 +1=u^2 +v^2$ over the integers

Published on 31 Oct 2020 - 11:04

111

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$m^n$ has exactly $9$ digits, all of these digits are distinct.

Published on 18 Nov 2020 - 17:13

84

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Two questions about a special function

Published on 27 Nov 2020 - 12:18

178

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Finding remainder using Fermat's Little Theorm

Published on 03 Dec 2020 - 18:00

114

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Number comparison: $5^{152}<2^{353}$ and $2^{1413}<3\cdot 5^{608}$

Published on 25 Mar 2026 - 17:39

77

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Are there more perfect powers of this form?

Published on 27 Dec 2020 - 17:12

896

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When do we have $(x y)^2 = x^2 y^2 $?

Published on 23 Feb 2026 - 17:24

72

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Power Tower and Finite Tetration

Published on 25 Jan 2021 - 6:47

714

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Solutions to $A^N+B^N=C^N \pm 1,\,$ for $N \geq 4$?

Published on 08 Feb 2021 - 1:04

109

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Why is the following for $B= A^x -(A-1)^x-(A-2)^x-(A-3)^x...(A-n)^x$ as long as $B ≥ 0$?

Published on 28 Apr 2021 - 1:10

49

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Why is it that $(n+(n+1)^2+(n+2)^3) \bmod 144 =0$ starting with $n=3$ and incrementing $n=n+6$?

Published on 08 May 2021 - 22:22

203

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Does every odd prime power divide a number of the form $\ n^{n-1}+n-1\ $?

Published on 14 Jul 2021 - 12:30

107

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Are there positive integers $a,b,c$ such that both $2a(b^c+1),2a(b^c-1)$ are perfect powers?

Published on 15 Jul 2021 - 13:00

List Question

$\lfloor x^n\rfloor\lfloor y^n\rfloor$ is a perfect square

Perfect powers in Horadam sequence

Solving $\tau^4 +1=u^2 +v^2$ over the integers

$m^n$ has exactly $9$ digits, all of these digits are distinct.

Two questions about a special function

Finding remainder using Fermat's Little Theorm

Number comparison: $5^{152}<2^{353}$ and $2^{1413}<3\cdot 5^{608}$

Are there more perfect powers of this form?

When do we have $(x y)^2 = x^2 y^2 $?

Power Tower and Finite Tetration

Solutions to $A^N+B^N=C^N \pm 1,\,$ for $N \geq 4$?

Why is the following for $B= A^x -(A-1)^x-(A-2)^x-(A-3)^x...(A-n)^x$ as long as $B ≥ 0$?

Why is it that $(n+(n+1)^2+(n+2)^3) \bmod 144 =0$ starting with $n=3$ and incrementing $n=n+6$?

Does every odd prime power divide a number of the form $\ n^{n-1}+n-1\ $?

Are there positive integers $a,b,c$ such that both $2a(b^c+1),2a(b^c-1)$ are perfect powers?

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