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Let $R$ be a commutative ring. Call a nonempty subset $F$ of $R$ a factroid if it is closed under sums and factors. That is: If $a,b \in F$, then $a+b \in F$, and If $a,b \in R$ with $a\in R$ ...

So, today I came up with a method for factoring polynomials whose coefficients are either $-1$ or $1.$ Let me explain with examples. Example No. 1. Factorize $P(x)=x^8+x^7+1$ Solution. It is known ...

Consider the following family of polynomials over $\mathbb{Q}$: $$f_n = x^n - x^{n-1} - \dots - 1$$ Notice that these polynomials satisfy the recurrence $$ f_{n+1} = x f_n - 1 $$ I would like to ...

I have two questions about the class of integer-coefficient polynomials all of whose roots are rational. I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!) ...