List questions from elementary-number-theory

Published on 16 Apr 2026 - 20:19

82

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Bijective function problem

Published on 11 Apr 2026 - 4:34

55

Views

Diophantine trouble

Published on 09 Apr 2026 - 4:35

1.3k

Views

Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

Published on 15 Apr 2026 - 18:39

253

Views

Has $\sigma\left(\sigma_0(n)^4\right)=n$ infinitely many solutions?

Published on 20 Apr 2026 - 5:52

245

Views

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

Published on 15 Apr 2026 - 20:09

84

Views

Order of congruences

Published on 12 Apr 2026 - 19:06

619

Views

prove that $\frac{a_n}{n}\rightarrow 1$: strange contest problem

Published on 17 Apr 2026 - 6:16

86

Views

Given a boolen hash function (based on XOR), find the $n^{th}$ key for a specific hash.

Published on 21 Apr 2026 - 7:52

371

Views

Which values for $x$ make $x(x + 180)$ a square?

Published on 16 Apr 2026 - 22:10

453

Views

Besides $3x - 1$, $5x + 1$, which variants of the $3x + 1$ problem have been proven conclusively one way or the other?

Published on 17 Apr 2026 - 1:09

55

Views

Relatively prime and divisibility proof

Published on 15 Apr 2026 - 12:01

209

Views

Zsigmondy's theorem

Published on 12 Apr 2026 - 6:06

105

Views

How does $\gcd(a^n, b^n) = 1 \implies \dfrac{a^n}{b^n}\not\in\mathbb{N}$?

Published on 16 Apr 2026 - 9:36

477

Views

GEB Why is it necessary for TNT-PROOF-PAIR{a,a'} to be represented in TNT?

Published on 20 Apr 2026 - 21:05

List Question

How to find the closest number to 100,000 and less than 100,000 which is a sum of two squares?

Bijective function problem

Diophantine trouble

Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

Has $\sigma\left(\sigma_0(n)^4\right)=n$ infinitely many solutions?

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

Order of congruences

prove that $\frac{a_n}{n}\rightarrow 1$: strange contest problem

Given a boolen hash function (based on XOR), find the $n^{th}$ key for a specific hash.

Which values for $x$ make $x(x + 180)$ a square?

Besides $3x - 1$, $5x + 1$, which variants of the $3x + 1$ problem have been proven conclusively one way or the other?

Relatively prime and divisibility proof

Zsigmondy's theorem

How does $\gcd(a^n, b^n) = 1 \implies \dfrac{a^n}{b^n}\not\in\mathbb{N}$?

GEB Why is it necessary for TNT-PROOF-PAIR{a,a'} to be represented in TNT?

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