List questions from elementary-number-theory

Published on 13 Apr 2026 - 19:53

36

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Halloween Trick or Treat how many in each neighborhood?

Published on 15 Apr 2026 - 20:42

440

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Asymptotics and bounds of $k$-divisor function $d_k(n)$

Published on 26 Apr 2026 - 0:52

204

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Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

Published on 16 Apr 2026 - 22:51

170

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Number of positive integral solutions $(x,y)$ of $x^2-y^2=12345678$

Published on 16 Apr 2026 - 4:16

1.3k

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Strong inductive proof of division algorithm (quotient with remainder)

Published on 10 Apr 2026 - 7:48

43

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Can a finite subset of integers ever be a maximal anti-ideal?

Published on 12 Apr 2026 - 0:59

90

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For any $a \in \Bbb{Z}$, can we always find two prime numbers $p, q$, such that $p - q \in (a)$?

Published on 10 May 2026 - 15:10

37

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Anti-ideals in $\Bbb{Z}$ form a matroid, so all maximal anti-ideals are in bijection?

Published on 10 May 2026 - 15:14

44

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The collection of anti-ideals of a ring forms a matroid?

Published on 10 May 2026 - 15:14

31

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Is the following fact about digital sums true?

Published on 18 Apr 2026 - 13:31

114

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n is primitive root for odd prime p. If -n is primitive root iff p = 4k+1 for some integer k

Published on 10 May 2026 - 18:03

368

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Show that ${240 \choose 120}$ is divisible by 242

Published on 13 Apr 2026 - 8:26

31

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How Close Can Numbers with Bounded Prime Factors Be?

Published on 09 Apr 2026 - 19:29

263

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Prove $(1+\sqrt{2})^k= \sqrt{n}+\sqrt{n-1}$

Published on 15 Apr 2026 - 19:48

List Question

How to solve $\,a^{100}\equiv 2,\ a^{101}\equiv 69\pmod{73}$

Halloween Trick or Treat how many in each neighborhood?

Asymptotics and bounds of $k$-divisor function $d_k(n)$

Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

Number of positive integral solutions $(x,y)$ of $x^2-y^2=12345678$

Strong inductive proof of division algorithm (quotient with remainder)

Can a finite subset of integers ever be a maximal anti-ideal?

For any $a \in \Bbb{Z}$, can we always find two prime numbers $p, q$, such that $p - q \in (a)$?

Anti-ideals in $\Bbb{Z}$ form a matroid, so all maximal anti-ideals are in bijection?

The collection of anti-ideals of a ring forms a matroid?

Is the following fact about digital sums true?

n is primitive root for odd prime p. If -n is primitive root iff p = 4k+1 for some integer k

Show that ${240 \choose 120}$ is divisible by 242

How Close Can Numbers with Bounded Prime Factors Be?

Prove $(1+\sqrt{2})^k= \sqrt{n}+\sqrt{n-1}$

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