Question

On some conjectures regarding repunits

score 226 · Answer 1 · 2026-04-13 03:02:00

226

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On some conjectures regarding repunits

Published on 13 Apr 2026 - 3:02

score 106 · Answer 2 · 2026-04-15 23:18:19

106

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Factoring (7) and (35) into products of prime ideals in the ring of integers of $\mathbb{Q}(\sqrt[3]{2})$

Published on 15 Apr 2026 - 23:18

score 116 · Answer 3 · 2026-04-11 11:18:10

116

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Does there exist a nontrivial prime power $q^k$ such that $\sigma(n^2)/n = q^k$ for some $n$?

Published on 11 Apr 2026 - 11:18

score 150 · Answer 4 · 2026-04-15 18:40:15

150

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Showing $X$ is irreducible in quotient of polynomial ring

Published on 15 Apr 2026 - 18:40

score 167 · Answer 5 · 2026-03-26 01:07:35

167

Views

Factorizing a quartic expression to show that it is a perfect square.

Published on 26 Mar 2026 - 1:07

score 55 · Answer 6 · 2026-04-12 12:56:53

55

Views

Simplifying algebraic expression with fraction of polynomials

Published on 12 Apr 2026 - 12:56

score 41 · Answer 7 · 2026-04-15 14:03:14

41

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How can we show $1<\gcd(b^s-1,N)<N$ here? (well-definedness of Shor's algorithm)

Published on 15 Apr 2026 - 14:03

score 54 · Answer 8 · 2026-04-14 12:45:05

54

Views

Notation for the number of $n$'s in $x$'s prime factorization

Published on 14 Apr 2026 - 12:45

score 86 · Answer 9 · 2026-04-14 05:06:52

86

Views

How to use the $x^n - a^n$ factoring pattern if $n$ is not an integer?

Published on 14 Apr 2026 - 5:06

score 71 · Answer 10 · 2026-04-16 13:58:04

71

Views

Factorize $x^8+17x^4+16x^2+17$ by hand

Published on 16 Apr 2026 - 13:58

score 51 · Answer 11 · 2026-04-14 16:33:29

51

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Let $M=2\times 3^2\times 5^3\times 7^4$. Let $a_1,a_2,...,a_{120}$ be the positive divisors of $M$. Calculate $\prod_{i=1}^{120} a_i$

Published on 14 Apr 2026 - 16:33

score 36 · Answer 12 · 2026-04-11 03:42:08

36

Views

What is the group theoretical term to describe a uniquely factorizable semigroup?

Published on 11 Apr 2026 - 3:42

score 85 · Answer 13 · 2026-04-13 23:12:34

85

Views

Factorize a composite number

Published on 13 Apr 2026 - 23:12

score 46 · Answer 14 · 2026-04-16 12:58:42

46

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If $ax^2+bx+c$ is irreductible, then exists constants $k_1,k_2,k_3$ such that $ax^2+bx+c = k_1((k_2x+k_3)^2+1).$

Published on 16 Apr 2026 - 12:58

score 52 · Answer 15 · 2026-04-17 01:56:27

52

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If $s = 4m - 3$, then $\sigma(p^s) = (1 + p^{2m-1})(1 + p + \ldots + p^{2m-2})$. Is there a similar factorization for $\sigma(q^t)$ when $t=4n$?

Published on 17 Apr 2026 - 1:56

List Question

On some conjectures regarding repunits

Factoring (7) and (35) into products of prime ideals in the ring of integers of $\mathbb{Q}(\sqrt[3]{2})$

Does there exist a nontrivial prime power $q^k$ such that $\sigma(n^2)/n = q^k$ for some $n$?

Showing $X$ is irreducible in quotient of polynomial ring

Factorizing a quartic expression to show that it is a perfect square.

Simplifying algebraic expression with fraction of polynomials

How can we show $1<\gcd(b^s-1,N)<N$ here? (well-definedness of Shor's algorithm)

Notation for the number of $n$'s in $x$'s prime factorization

How to use the $x^n - a^n$ factoring pattern if $n$ is not an integer?

Factorize $x^8+17x^4+16x^2+17$ by hand

Let $M=2\times 3^2\times 5^3\times 7^4$. Let $a_1,a_2,...,a_{120}$ be the positive divisors of $M$. Calculate $\prod_{i=1}^{120} a_i$

What is the group theoretical term to describe a uniquely factorizable semigroup?

Factorize a composite number

If $ax^2+bx+c$ is irreductible, then exists constants $k_1,k_2,k_3$ such that $ax^2+bx+c = k_1((k_2x+k_3)^2+1).$

If $s = 4m - 3$, then $\sigma(p^s) = (1 + p^{2m-1})(1 + p + \ldots + p^{2m-2})$. Is there a similar factorization for $\sigma(q^t)$ when $t=4n$?

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