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Question 1

3votes

2answers

121views

Conjecture: $\quad C_{2n-1}=\frac{1}{2+\frac{3}{4+\frac{5}{6+\frac{7}{\dots(2n-2)+(2n-1)}}}}=\frac{p}{q} \implies \frac{p+q}{2} \mid (2n-1)!!$

For any $n>0$,Consider the fraction:$$ C_{2n-1}=\frac{1}{2+\frac{3}{4+\frac{5}{6+\frac{7}{\dots(2n-2)+(2n-1)}}}}$$Let $ N_{2n-1}$and $D_{2n-1}$ be the lowest numerator and denominator of the $...

Mr. Curious

321

askedyesterday

Question 2

4votes

1answer

210views

A $3$-adic valuation regarding $ C_n = \frac{1}{3+\frac{2}{5+\frac{3}{7+\frac{4}{11+\frac{5}{13+\dots\frac{n}{p_n}}}}}} $ is always $1$?

My previously asked question motivated me to ask this question.For $n^{th}$ odd prime $p_n$,We define the following fraction:$$C_n = \frac{1}{3+\frac{2}{5+\frac{3}{7+\frac{4}{11+\frac{5}{13+\dots\...

Mr. Curious

321

askedNov 25 at 17:18

Question 3

8votes

1answer

153views

The numerator of $ C_{n>4} = \frac{1}{3+\frac{5}{7+\frac{11}{13+\frac{17}{19+\frac{23}{29+\dots p_n}}}}} $ is always divisible by $17$?

For $n^{th}$ odd prime $p_n$,We define the following fraction:$$C_n = \frac{1}{3+\frac{5}{7+\frac{11}{13+\frac{17}{19+\frac{23}{29+\dots p_n}}}}}$$We also define $N_n$ as the numerator of the $\...

Mr. Curious

321

askedNov 25 at 10:47

Question 4

-4votes

0answers

88views

Integer sequence plus 41 [closed]

Consider the function $F:\mathbb{N}\to\mathbb{N}$ such that $F(n)=n^2+n+41$.Evidence suggests that if $n\le6.618.260$, then $F(n)$ has at most 7 different prime factors. I wonder what would be a good ...

Cristian Baeza

965

askedNov 24 at 22:30

Question 5

0votes

1answer

60views

Test if a set A is a subset of a set B using prime factors

Say I want a space efficient way of representing documents and queries as sets of terms, where I want to be able to efficiently see if a query is a subset of a document (ie all the terms in the query ...

bobpoekert

103

askedNov 22 at 16:40

Question 6

1vote

0answers

58views

How many consecutive integers can have all their prime divisors in a set $P$ of size $k$? [closed]

Let $P$ be a finite set of primes of cardinality $k$.Consider the set $A(P) = \{ n \ge 1 : \text{every prime dividing } n \text{ is in } P \}$.Let $L(P)$ be the largest number of consecutive ...

user1714459

11

askedNov 17 at 12:25

Question 7

1vote

0answers

33views

what is the minimum number of video frames to have a clean loop for a song with a particular tempo? [duplicate]

It occurred to me to ask this question of the video SE community, but I worry about their mathematical prowess, and I'm looking for a really clean formula or algorithm for this problem.I have a song ...

S. Imp

111

askedOct 23 at 20:02

Question 8

0votes

1answer

134views

Closed formula : given a product of $2$ primes what is their difference?

BackgroundGiven $2$ primes $p_1$ and $p_2$ and their product $c= p_1p_2$. What is the best approximation of the difference $\Delta = p_2 - p_1$ with $p_2 \geq p_1$ in terms of $c$.We start with:$$ \...

More Anonymous

1,191

askedOct 11 at 5:34

Question 9

2votes

1answer

81views

Example that $\dim_{A/\mathfrak{p}}(B/\mathfrak{p}B)=[L:K]$ fails in an $AKLB$ setup.

Consider the $AKLB$ setup: $A$ is a Dedekind domain, $K=\operatorname{Frac}(A)$, $L$ is a finite extension of $K$ (not necessarily separable), and $B$ is the integral closure of $A$ in $L$. Then we ...

Jianing Song

2,783

askedOct 10 at 18:23

Question 10

5votes

1answer

143views

Is there a $n$-sided polygon with side lengths $1, \dots, n$ and equal angles, where $n$ is the power of a prime?

This question arose while solving the following problem:Prove that for every positive integer $n$ such that $n$ isn't the power of a prime, there is a $n$-sided polygon with all its angles equal and ...

mlg

363

askedOct 5 at 11:54

Question 11

4votes

0answers

189views

Solutions to a relation between $\varphi(n)$ and $n$

I know of different types of solutions to relations between $\varphi(n)$ and $n$, e.g. the classical question to find all positive integers $n$ for which $\phi(n)$ divides $n$. But the following ...

pi in the sky

41

askedOct 4 at 13:47

Question 12

0votes

0answers

49views

Confusion about CRT step of square root algorithm in NFS

I am trying to implement the square root step of the GNFS followingBriggs, The Use of the Number Field Sieve in the Computation of Square Roots, in particular Section 4.6 and Example 5.11.The ...

Grazka

1

askedSep 22 at 7:48

Question 13

1vote

0answers

74views

Prime polygons and the constant‑sum property in Viviani‑type theorems

Viviani's theorem states that the sum of the perpendicular distances from any point inside a given equilateral trianlge to its three sides is constant. This idea has various extentions under the ...

Mohammad Mahdi Nasimi

31

askedSep 13 at 21:50

Question 14

-5votes

1answer

140views

Why the number of n satisfying $Ω(n)=k-t$ within the interval $(2^k,2^{k+1}]$ becomes constant after several terms?

Background:The function $\Omega(n)$ is defined as the sum of the exponents of all prime factors in the prime factorization of a positive integer n.Why the count of $n$ satisfying $Ω(n)=k-t$ within ...

Constantine

7

askedSep 9 at 8:24

Question 15

1vote

0answers

49views

Is this a contradiction-free proof of if $n$ is not the $m$-th power of an integer then $n^{1/m}$ is irrational.

This is another oneof my mathematical musingsthat are probably well knownbut I came up with myself.I was playing around withsome of the proofs that$\sqrt{2}$ is irrationaland noticed thatthey ...

marty cohen

111k

askedJul 25 at 0:08

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Questions tagged [prime-factorization]

Conjecture: $\quad C_{2n-1}=\frac{1}{2+\frac{3}{4+\frac{5}{6+\frac{7}{\dots(2n-2)+(2n-1)}}}}=\frac{p}{q} \implies \frac{p+q}{2} \mid (2n-1)!!$

A $3$-adic valuation regarding $ C_n = \frac{1}{3+\frac{2}{5+\frac{3}{7+\frac{4}{11+\frac{5}{13+\dots\frac{n}{p_n}}}}}} $ is always $1$?

The numerator of $ C_{n>4} = \frac{1}{3+\frac{5}{7+\frac{11}{13+\frac{17}{19+\frac{23}{29+\dots p_n}}}}} $ is always divisible by $17$?

Integer sequence plus 41 [closed]

Test if a set A is a subset of a set B using prime factors

How many consecutive integers can have all their prime divisors in a set $P$ of size $k$? [closed]

what is the minimum number of video frames to have a clean loop for a song with a particular tempo? [duplicate]

Closed formula : given a product of $2$ primes what is their difference?

Example that $\dim_{A/\mathfrak{p}}(B/\mathfrak{p}B)=[L:K]$ fails in an $AKLB$ setup.

Is there a $n$-sided polygon with side lengths $1, \dots, n$ and equal angles, where $n$ is the power of a prime?

Solutions to a relation between $\varphi(n)$ and $n$

Confusion about CRT step of square root algorithm in NFS

Prime polygons and the constant‑sum property in Viviani‑type theorems

Why the number of n satisfying $Ω(n)=k-t$ within the interval $(2^k,2^{k+1}]$ becomes constant after several terms?

Is this a contradiction-free proof of if $n$ is not the $m$-th power of an integer then $n^{1/m}$ is irrational.

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