Let $p$ be a prime. Let $f(x) = 3x+1$ and $g(x) = 6x+1$. Show that if $f(x) = p$, then $g(y) = p$.
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
131488
Show that $p^3+4$ is prime
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
21846
Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.