Factorization $a^x-1 | (a^x)^k - 1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
108187
When does $p^2$ divide $an^k + bp$?
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
66558
Find the value of $a$ and $b$ if $x+1$ and $x−2$ are factors of $ax^3−4x^2+bx−12$
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
47299
Factorize $x^8-x$ over $F_3$ and $F_{81}$
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
8504
Factoring $x^n + y^n$ over the integers
80144
Prove that $x-1$ divides $x^n-1$
113230
How can we factor $ q^4 + q^2 + 1$
62980
How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$?
21439
For which $k\in \Bbb N$ does $x^2+x+1$ divide $ (x + 1)^{2k}+x^{2k} + 1$?
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
9997
For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$