# Questions tagged [coprime]

Use this tag for questions related to integers such that the only positive integer that divides them is 1.

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### What are all simplifiable fractions k/N (0<=k<=N) called and how can one generate them?

The problem I am trying to solve is as follows: Take a positive integer $N$. Give the function $f$, such that $f(N)$ generates the sequence of all fractions $\frac{k}{N}$ where $(0 \le k \le N)$ such ...
44 views

### Coprimality of certain linear combinations of Fibonacci numbers (integer coefficients)

Let $G_k(m,n)=m\,F_k+n\,F_{k-1}$, where $k,m,n$ are any integers and $(F_k)_{k\in\mathbb{Z}}$ is the extended Fibonacci sequence defined by $F_0=0,F_1=1,F_{k+2} = F_{k+1}+F_k$ for all $k\in\mathbb{Z}.$...
26 views

### Prime factors of a number in the form $2^n+1$

What is the gcd of $2^{55} +1$ and $165$? This question was asked in KVPY 2019 SA.
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### Maximum Number of Consecutive Numbers with Limited Prime Factors

I understand that the maximal distance between consecutive coprimes to a primorial $P_n\#$ has order $O(P_n^2)$. My question is, given that you can ONLY use prime numbers less than X and no others, ...
31 views

### Sum and product of coprime numbers

Lets suppose we have $a$ and $b$ which are natural numbers and coprime. Are $a+b$ and $a\cdot b$ then coprime to each other? I can't find any information on that on the internet so I'd be thankful ...
11 views

### Article: Invariant Sylow subgroups and solvability of finite groups - Antonio Beltran.

This is a article which Antonio Beltran. I'm reading lemma 2.2.b). I see that: "Lemma 2.2. Suppose that A is a finite group acting coprimely on a finite group G, and let $C = C_G(A)$. Then, for every ...
23 views

### Given d = gcd(c,n), why there exists relatively prime integers r and s, such that c = rd and n = sd [duplicate]

Given $d = gcd(c,n)$, why there exist relatively prime integers r and s, such that $c = rd$ and $n = sd$?
37 views

### How to find the number of coprime numbers to $100$?

Is there a way to find the number of coprime numbers ($2$ digit numbers) to $100$ without writing them?
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### Number Theory Question: If $m$ and $n$ are coprime, prove $m| (x-a)$ and $n | (x-b)$

I have this math problem I'm struggling to solve. If $m$ and $n$ are co-prime, prove $m|(x-a)$ and $n|(x-b)$ for some $x\in\mathbb{Z}$ and all $a ,b\in\mathbb{Z}$ Thank you!
71 views

### Find the thousandth number in the sequence of numbers relatively prime to $105$.

Suppose that all positive integers which are relatively prime to $105$ are arranged into a increasing sequence: $a_1 , a_2 , a_3, . . . .$ Evaluate $a_{1000}$ By inclusion exclusion principle I ...
34 views

### Stuck on Consecutive Moduli Selection (Residue Number System)

I'm preparing for my final year project in school and i plan on working on the implementation of Residue Number System in Image Processing. I found this thesis online by Pallab Maji here: http://...
113 views

### to find co-prime with 7 from [-10,10]

How many integers in [-10,10] are co-prime with 7? I find that prime belongs to N, so my answer is 9(1,2,3,4,5,6,8,9,10). can you give me advice?
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### Showing that $\frac{(m+n-1)!}{m!n!}\in\mathbb{Z}$, if $m,n$ coprime (homework problem) [duplicate]

My attempt: assume $m> n$. Since $\binom{x}{y}\in\mathbb{Z}$ for every $x\geq y$, we have that $$K:=\binom{m+n-1}{n}=\frac{(m+n-1)!}{(m-1)!n!}\in\mathbb{Z}$$ It remains to show that $m|K$. I know ...
34 views

### On the co-primality of bracelet-type binary numbers

Let an integer N be the number of digits imprinted on a bracelet, which can come in two values, 1 and 0. You can produce a binary number by writing down the 1's and 0's on the bracelet from left to ...
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### Divisibility and number theory in terms of a and b

Are there infinitely many pairs of $(a, b)$ of relatively prime integers $a > 1$ and $b > 1$ such that $a^b+b^a$ is divisible by $a+b$? I've spent almost two hours on this question to no avail. ...
45 views