# 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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### Infinite numbers of coprime pairs $k(6k-1)$.

This question leads to the following consideration. Are there infinite number of pairs of the form $\big(j(6j-1),\, k(6k−1)\big)$ where $j<k$ such that $j(6j-1)$ and $k(6k−1)$ are coprime? One ...
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### Equivalent integral quadratic forms properly represent the same integers

Definitions: An integral quadratic form (IQF) is some instance of $f(x,y)=ax^2+bxy+cy^2$, where $a,b,c \in \mathbb{Z}$. Let $f(x,y),g(x,y)$ denote IQFs. We say $f(x,y)$ and $g(x,y)$ are properly ...
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### PHI function to list relative primes

I am using a website called dcode to input numbers into the PHI function, and then receive an output of numbers relatively prime with my input. The website, unfortunately, limits output to just 500 ...
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### Expressing any even natural number as a sum of primorials with coefficients

I'm having a hard time trying to solve the following problem: Given any random even natural number, $x$, prove that it can or cannot be written as the product of some integer, $b$, times the primorial ...
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### Conjecture: Every $n \geq 20 \in \mathbb{N}$ can be written as a sum of three integers $(\geq 2)$ that are pairwise coprime

This question on the sum of pairwise prime numbers piqued my interest, and I started looking at what numbers can be written as the sum of three pairwise coprime numbers (excluding $1$):  \begin{...
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