List questions from number-theory

Published on 01 May 2026 - 13:00

51

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In how many ways can I decompose $n \equiv \pm k \mod{m}$ in a sum of numbers also congruent to $\pm k \mod m$?

Published on 15 Apr 2026 - 18:58

106

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Does the equation $q^2\, n(n+1) = p^2\, m(m+1)$ have solutions only if $m(m+1) = q^2\, k(k+1)$, $k<m$?

Published on 18 Apr 2026 - 5:35

433

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In the Diophantine equation, 5x + 17y = c

Published on 17 Apr 2026 - 3:21

844

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Diophantine equation $a^2+b^2+c^2=a^2b^2$

Published on 15 Apr 2026 - 12:44

151

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Derive prime-identifying functions from inverse Vandermonde and Bernoulli numbers

Published on 29 Apr 2026 - 12:27

295

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$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

Published on 11 Apr 2026 - 12:08

236

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System of Diophantine equations $a^2+b^2=2x^2+1,c^2+d^2=2y^2+1,ac-bd=1$ has no natural solutions.

Published on 15 Apr 2026 - 5:26

300

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Reference for Dedekind's Example of a Non-monogenic Field

Published on 11 Apr 2026 - 1:17

612

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number of square roots of unity modulo a prime power

Published on 16 Apr 2026 - 7:13

75

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Do there exist distinct integers $p$ and $q$ such that $\dfrac{p}{n} = \dfrac{q}{n+1}$ for some integer $n$?

Published on 30 Apr 2026 - 9:41

185

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Are there infinitely many prime numbers of the form $p^2+4$ with $p$ prime?

Published on 14 Apr 2026 - 20:58

51

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Inference of a condition

Published on 13 Apr 2026 - 6:21

367

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Order of an element modulo $n$ divides $\varphi(n)/2$.

Published on 30 Apr 2026 - 9:41

319

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Number of incongruent integers that have a given order modulo p.

Published on 15 Apr 2026 - 22:11

List Question

ABC conjecture Proof

In how many ways can I decompose $n \equiv \pm k \mod{m}$ in a sum of numbers also congruent to $\pm k \mod m$?

Does the equation $q^2\, n(n+1) = p^2\, m(m+1)$ have solutions only if $m(m+1) = q^2\, k(k+1)$, $k<m$?

In the Diophantine equation, 5x + 17y = c

Diophantine equation $a^2+b^2+c^2=a^2b^2$

Derive prime-identifying functions from inverse Vandermonde and Bernoulli numbers

$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

System of Diophantine equations $a^2+b^2=2x^2+1,c^2+d^2=2y^2+1,ac-bd=1$ has no natural solutions.

Reference for Dedekind's Example of a Non-monogenic Field

number of square roots of unity modulo a prime power

Do there exist distinct integers $p$ and $q$ such that $\dfrac{p}{n} = \dfrac{q}{n+1}$ for some integer $n$?

Are there infinitely many prime numbers of the form $p^2+4$ with $p$ prime?

Inference of a condition

Order of an element modulo $n$ divides $\varphi(n)/2$.

Number of incongruent integers that have a given order modulo p.

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