# Questions tagged [factoring]

For questions about finding factors of e.g. integers or polynomials

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### Two reducible polynomials over $\mathbb Q[X]$

I`ve asked it here before, but figured out that there was a minor typo, and as I didnt received any answer I deleted my old question and I am posting again. I apologize if it is elementary, but here ...
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### If $f\in \mathbb{Q}[x,y]$ factors in some field extension of $\mathbb{Q}$, then it also factors in some finite extension of $\mathbb{Q}$? [closed]

If $f(x,y)\in \mathbb{Q}[x,y]$ factors non-trivially (as a product of two non-constant polynomials) in some field extension of $\mathbb{Q}$, then does it also factor non-trivially in some finite field ...
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### Divisibility (algebraic expressions) - can this be generalised?

Consider the expression $a^{3}+b^{3}+c^{3}-3abc$. It is divisible by $(a+b+c)$ Now, consider the expression $a^{3}+b^{3}+c^{3}+d^{3}-3(abc+abd+acd+bcd)$ It is divisible by $(a+b+c+d)$ Can this be ...
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### Bound of squarefree part of an integer

I am studying the paper DIOPHANTINE EQUATIONS OF THE FORM $F(X) = G(Y)$ - AN EXPOSITION which discusses the result of Erdos and Selfridge. I am unable to understand the highlighted statement ''Clearly ...
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### Difference between polynomials with integer and non integer coefficiants regarding number of roots of polynomial [duplicate]

There is a prior question to show that polynomial of degree 7 with all integer coefficiants has 7 integer values $P(x1,x2...x7)=+-1$ cant be expressed as product of two polynomials with integer ...
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### General formula for factoring $ax^2+bx+c$ [duplicate]

I watched a YouTube video on factoring (namely, 100 trinomial factoring (Dedicated to Mr. Hill) by blackpenredpen) and was curious about the math behind the method he first shows around 12:15. Is ...
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### Coefficients of some polynomials factorization

EDITED If anyone is interested in this question, now there are OEIS draft and repository with detailed data. Let $n,b\in\mathbb{N}$ and $P_{n_b}$ is polynomial whose coefficients are digits of $n$ ...
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### Factorizing $AMA^T+N=WW^T$ efficiently.

This question is related to this question with a slightly more general setting. A good speedup on this could improve performances of a decision process in multi-objective optimization that I designed. ...
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### What is the relation between these two descriptions of General Number Field Sieve?

I am reading about General Number Field Sieve (GNFS) algorithm and its implementations, and the literature seems to have two different versions of the algorithm, but I can't find how these two are ...
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### Find all $x \in \mathbb{R}$ such that $1+\sqrt{1-\frac{1}{x}}+\sqrt{x-\frac{1}{x}}=x^2$.

This problem was posed by a friend of mine. He's got it from a social media post. We don't know how to solve it, but there are similar types of questions in this website, whose techniques I've tried ...
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### Factoring bivariate polynomials

Consider the following bivariate polynomial $$P (x,y) = \sum_{m=0}^{2}\sum_{n=0}^{2} a_{m,n} x^{m} y^{n}$$ where the coefficients $a_{m,n}$ can be complex numbers. I was wondering if there are any ...
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### How can this sinh curve be massaged?

Sorry I'm new here so I don't know how to use the math symbols yet but I would really appreciate some help with something I'm stuck on. How can this equation:  𝑦(𝑥)=𝑥 \sinh(\sinh^{-1}(𝑦_0)−\rho \...
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### Factorization of $f(x)=x$ in $\Bbb{Z}/n\Bbb{Z}[x]$ where $n$ is the product of $k$ distinct primes (considering $\Bbb{Z}/30\Bbb{Z}[x]$ as example)

Intro This is the final part of the problem 9.4.20 (e), (d) from Dummit and Foote's Abstract Algebra. They formulate it as "Determine all the factorizations of $f(x)=x$ in $\Bbb{Z}/n\Bbb{Z}[x]$ ...
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### Factoring a year to get a date

Let's factor 2024: $2024=8\times 11\times 23$. So we can make a date: 8/11/23, or August 11, 2023. Or we could also make 11/8/23, November 8, 2023 (if you live in Europe, they will be switched). ...
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