List questions from perfect-powers

Published on 18 May 2019 - 9:05

91

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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 06 Jun 2019 - 12:03

612

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

Published on 09 Jun 2019 - 23:19

225

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

Published on 13 Jun 2019 - 20:47

145

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

Published on 14 Jun 2019 - 20:42

467

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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 27 Jun 2019 - 12:23

144

Views

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

Published on 28 Jun 2019 - 4:01

606

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

Published on 01 Jul 2019 - 2:38

100

Views

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

Published on 20 Jul 2019 - 9:49

78

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Are there forced factors of numbers of this kind?

Published on 12 Aug 2019 - 10:36

642

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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 23 Aug 2019 - 6:56

994

Views

Pythagorean triple with hypotenuse a power of $2$

Published on 23 Aug 2019 - 12:33

102

Views

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

Published on 30 Aug 2019 - 21:13

161

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

Published on 03 Sep 2019 - 0:57

71

Views

Solving Diophantine Equations Involving Exponentials as Positive Integers

Published on 05 Sep 2019 - 10:52

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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