List questions from perfect-powers

Published on 05 Mar 2022 - 12:58

446

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How close is an odd power of two to a perfect square?

Published on 05 Mar 2022 - 19:28

67

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Number Theory Problem: Find a perfect power k^m > 1 where k, m, k^m do not contain 2 in their decimal digits, nor do share any decimal digit.

Published on 15 Apr 2022 - 9:52

375

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Prove that we can express $n^k$ as a sum of $n$ consecutive odd natural numbers

Published on 24 Apr 2022 - 12:43

98

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To prove that irrational powers of 1 is equal to 1

Published on 12 May 2022 - 14:33

32

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Formula for working out the greatest power that another number is divisible by

Published on 30 Jul 2022 - 14:24

46

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Finding three perfect complex powers with equal norm and cancelling imaginary parts

Published on 19 Aug 2022 - 1:39

494

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Can $5^n+6^n+10^n$ be a perfect power?

Published on 18 Sep 2022 - 19:32

699

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Potential solution to Sloane's "Powers of 2" problem?

Published on 22 Sep 2022 - 2:01

106

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How to make graphs that avoid certain sub-graphs and have as many edges as possible?

Published on 27 Sep 2022 - 17:49

33

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Finding the smallest perfect power in a range

Published on 16 Oct 2022 - 4:51

26

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Is there an analogue to Bertrand's Postulate for primes for perfect powers?

Published on 16 Oct 2022 - 13:46

143

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$(a^n-1)(b^n-1)$ can't be a square for all $n$ unless $ab$ is a square

Published on 20 Dec 2022 - 21:03

552

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Can $\,9\!\cdot\!10^n+4\,$ be a perfect square?

Published on 21 Jan 2023 - 12:32

160

Views

Can $300$…$04$ be a perfect square?

Published on 22 Jan 2023 - 22:46

List Question

Self-powers residues

How close is an odd power of two to a perfect square?

Number Theory Problem: Find a perfect power k^m > 1 where k, m, k^m do not contain 2 in their decimal digits, nor do share any decimal digit.

Prove that we can express $n^k$ as a sum of $n$ consecutive odd natural numbers

To prove that irrational powers of 1 is equal to 1

Formula for working out the greatest power that another number is divisible by

Finding three perfect complex powers with equal norm and cancelling imaginary parts

Can $5^n+6^n+10^n$ be a perfect power?

Potential solution to Sloane's "Powers of 2" problem?

How to make graphs that avoid certain sub-graphs and have as many edges as possible?

Finding the smallest perfect power in a range

Is there an analogue to Bertrand's Postulate for primes for perfect powers?

$(a^n-1)(b^n-1)$ can't be a square for all $n$ unless $ab$ is a square

Can $\,9\!\cdot\!10^n+4\,$ be a perfect square?

Can $300$…$04$ be a perfect square?

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