Methods to prove $\frac{21n + 4}{14n + 3}$ is irreducible for every natural number $n$
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
123820
Guess the formula for $\sum\frac 1{(4n-3)(4n+1)}$ and prove by induction
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
153062
Question about irreducible Gaussian integers
144310
How would you prove that $\lim\limits_{n\to\infty}(\sqrt{4n^2+n}-2n)=\frac14$?
111938
How do I find a flaw in this false proof that $7n = 0$ for all natural numbers?
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
4530
For which natural numbers are $\phi(n)=2$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
54055
Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
156786
Show that $15\mid 21n^5 + 10n^3 + 14n$ for all integers $n$.
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
79564
Algorithm to find the irreducible polynomial
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
64878
Is this polynomial irreducible in $\mathbb{Q}$?
34387
Is the number of irreducibles in any number field infinite?
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$