List questions from examples-counterexamples

251

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Conjecture: $n>2$ is prime iff $\sum_{k=1}^{n-1}\left(3^k-2\right)^{n-1} \;\equiv\; n \cdot 2^{n-1}-1 \pmod{\frac{3^n-1}{2}}$

Published on 26 Mar 2026 - 1:11

514

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Conjectured primality tests for specific classes of $k\cdot b^n \pm 1$

Published on 23 Mar 2026 - 0:04

440

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Find a function for which integral does not exist but converges as a limit of a sequence

Published on 03 Feb 2019 - 23:34

113

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Does $\nabla g=\omega(\cdot) g$ imply $\nabla$ is metric w.r.t a conformal rescaling of $g$?

Published on 25 Mar 2026 - 18:50

115

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Open set in terms of nets

Published on 26 Mar 2026 - 19:56

1k

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Non-existence of the potential function

Published on 26 Mar 2026 - 19:38

446

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Counterexample to Lie's second theorem for SO(3)

Published on 07 Feb 2019 - 23:02

121

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Stable and unstable manifolds that are tangent to each other in a continuous dynamical system?

Published on 08 Feb 2019 - 3:34

176

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Counterexample for $\lim_{n\to\infty} (a_{n-1}-a_n) = 0 \Rightarrow a_n$ converges

Published on 08 Feb 2019 - 18:52

882

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Measurable function that does not map a set of measure zero to a set of measure zero

Published on 09 Feb 2019 - 20:41

42

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Is closedness assumption is essential in following argument?

Published on 10 Feb 2019 - 6:10

538

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Star-convex is not convex?

Published on 10 Feb 2019 - 8:10

332

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Trace of a filter

Published on 11 Feb 2019 - 5:18

74

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Is a completely regular space whose convergent sequences are eventually constant discrete?

Published on 25 Mar 2026 - 6:31

363

Views

Are metrics uniformly equivalent if and only if they have the same zero-distance sets?

Published on 23 Feb 2026 - 2:47

List Question

Conjecture: $n>2$ is prime iff $\sum_{k=1}^{n-1}\left(3^k-2\right)^{n-1} \;\equiv\; n \cdot 2^{n-1}-1 \pmod{\frac{3^n-1}{2}}$

Conjectured primality tests for specific classes of $k\cdot b^n \pm 1$

Find a function for which integral does not exist but converges as a limit of a sequence

Does $\nabla g=\omega(\cdot) g$ imply $\nabla$ is metric w.r.t a conformal rescaling of $g$?

Open set in terms of nets

Non-existence of the potential function

Counterexample to Lie's second theorem for SO(3)

Stable and unstable manifolds that are tangent to each other in a continuous dynamical system?

Counterexample for $\lim_{n\to\infty} (a_{n-1}-a_n) = 0 \Rightarrow a_n$ converges

Measurable function that does not map a set of measure zero to a set of measure zero

Is closedness assumption is essential in following argument?

Star-convex is not convex?

Trace of a filter

Is a completely regular space whose convergent sequences are eventually constant discrete?

Are metrics uniformly equivalent if and only if they have the same zero-distance sets?

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