If $a,b$ is an $R$-sequence, then $ax-b$ is prime (Eisenbud, Exercise 10.4)
13174
Show that $A[X]/(aX+b)$ is an integral domain
50266
In the following figure prove that: $AK||BC$
69582
Is it true that: $a+bi$ is prime in $\mathbb{Z}[i]$ if and only if $a^2+b^2$ is prime in $\mathbb{Z}$
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
61899
Prove that the language $\{bin(p) \mid p\ \text{is prime}\}$ is not regular (prime numbers)
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
89329
If a and b are relatively prime and ab is a square, then a and b are squares.
125499
Find this sequence $a_{i}$ such $\gcd{(a_{i},a_{j})}=\gcd{(i,j)}$
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
7899
Show that if $p$ is prime then $\Bbb Z_p$ is a field
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
59885
Proof Verification - Every sequence in $\Bbb R$ contains a monotone sub-sequence
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set