List questions from perfect-powers

Published on 16 Apr 2026 - 7:47

95

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Can any Power function (whose base is not zero) , e.g. $2^{n}$, be defined arithmetically (i.e. using addition and multiplication only)?

Published on 10 May 2026 - 16:31

615

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$A^X+B^Y=C^Z\pm 1$ Beal's conjecture "almost" solutions

Published on 15 Apr 2026 - 11:06

228

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Integer solutions to $2^x-1=3^y$.

Published on 14 Apr 2026 - 23:19

150

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Perfect powers of the form $2^n\pm n$?

Published on 17 Apr 2026 - 12:10

470

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If $U, V, W$ and m are natural numbers such that $U^m + V^m = W^m$ , then $m$< max$( U , V ,W)$

Published on 15 Apr 2026 - 18:03

147

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Are there nontrivial perfect powers of integers that are nontrivial repdigits?

Published on 11 Apr 2026 - 22:30

609

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How many zeros in the decimal representation of $5^n$?

Published on 10 Apr 2026 - 18:50

103

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Can $n$ be expressed as $a^b-c^d$, where $a,b,c,d,$ and $n$ are natural numbers, not necessary distinct?

Published on 14 Apr 2026 - 20:09

81

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Are there forced factors of numbers of this kind?

Published on 08 Apr 2026 - 21:46

645

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Find all natural number $n$ for which $3^9+3^{12}+3^{15}+3^n$ is a perfect cube.

Published on 16 Apr 2026 - 18:59

997

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Pythagorean triple with hypotenuse a power of $2$

Published on 09 Apr 2026 - 16:31

105

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Conjecture That The Only Nearly Perfect Numbers Are The Powers Of 2

Published on 12 Apr 2026 - 11:16

164

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What is the $n^\text{th}$ perfect power, $P(n)$?

Published on 11 Apr 2026 - 14:03

74

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Solving Diophantine Equations Involving Exponentials as Positive Integers

Published on 17 Apr 2026 - 3:01

List Question

Is there any $k$ , for which we can prove that $n^n+k$ is never prime?

Can any Power function (whose base is not zero) , e.g. $2^{n}$, be defined arithmetically (i.e. using addition and multiplication only)?

$A^X+B^Y=C^Z\pm 1$ Beal's conjecture "almost" solutions

Integer solutions to $2^x-1=3^y$.

Perfect powers of the form $2^n\pm n$?

If $U, V, W$ and m are natural numbers such that $U^m + V^m = W^m$ , then $m$< max$( U , V ,W)$

Are there nontrivial perfect powers of integers that are nontrivial repdigits?

How many zeros in the decimal representation of $5^n$?

Can $n$ be expressed as $a^b-c^d$, where $a,b,c,d,$ and $n$ are natural numbers, not necessary distinct?

Are there forced factors of numbers of this kind?

Find all natural number $n$ for which $3^9+3^{12}+3^{15}+3^n$ is a perfect cube.

Pythagorean triple with hypotenuse a power of $2$

Conjecture That The Only Nearly Perfect Numbers Are The Powers Of 2

What is the $n^\text{th}$ perfect power, $P(n)$?

Solving Diophantine Equations Involving Exponentials as Positive Integers

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