List questions from conjectures

Published on 08 Dec 2020 - 21:20

119

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Is it true that every closed formula is decidable? Why?

Published on 23 Feb 2026 - 13:34

163

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Bézout giving some spare coins to Frobenius? (the Coin Problem)

Published on 29 Mar 2026 - 14:02

92

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Is there always a prime $p$ which falls short of $2^n$ by at most a square-root factor?

Published on 26 Mar 2026 - 20:16

87

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Conjecture : A lower bound for the prime counting function .

Published on 30 Mar 2026 - 5:11

69

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Can you prove this number theory conjecture?

Published on 18 Dec 2020 - 5:18

142

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Does the Bunyakovsky conjecture apply for every cyclotomic polynomial?

Published on 28 Mar 2026 - 4:33

176

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Conjecture regarding the sum of prime factors of $x!$ and $(x-1)!$?

Published on 29 Dec 2020 - 21:01

281

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Sums of integer powers similar to Prouhet–Tarry–Escott problem

Published on 02 Jan 2021 - 22:10

370

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A curious infinite product of factorials

Published on 02 Apr 2026 - 17:43

69

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Integer solutions to $r\cdot a^2+t=s\cdot b^2$ forms sequences with $a_{n+1}\cdot b_n-a_n\cdot b_{n+1}$ is invariant

Published on 12 Jan 2021 - 12:24

132

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On Andrica's conjecture.

Published on 15 Jan 2021 - 21:02

69

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Can you spot the mistake here?

Published on 16 Jan 2021 - 20:34

439

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Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number?

Published on 27 Mar 2026 - 13:10

64

Views

Let $n=am+r$ with $m \ge a>5$ and $r \ge 0$. Prove that $\phi(n) \ge m$

Published on 26 Jan 2021 - 15:32

List Question

Conjecture: any factorial is a sum of two Jordan-Polya numbers.

Is it true that every closed formula is decidable? Why?

Bézout giving some spare coins to Frobenius? (the Coin Problem)

Is there always a prime $p$ which falls short of $2^n$ by at most a square-root factor?

Conjecture : A lower bound for the prime counting function .

Can you prove this number theory conjecture?

Does the Bunyakovsky conjecture apply for every cyclotomic polynomial?

Conjecture regarding the sum of prime factors of $x!$ and $(x-1)!$?

Sums of integer powers similar to Prouhet–Tarry–Escott problem

A curious infinite product of factorials

Integer solutions to $r\cdot a^2+t=s\cdot b^2$ forms sequences with $a_{n+1}\cdot b_n-a_n\cdot b_{n+1}$ is invariant

On Andrica's conjecture.

Can you spot the mistake here?

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number?

Let $n=am+r$ with $m \ge a>5$ and $r \ge 0$. Prove that $\phi(n) \ge m$

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