Suppose that both $p$ and $p^2 +2$ are prime numbers. Show that $p=3$.
58114
For which primes p is $p^2 + 2$ also prime?
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
85006
If $a$ and $b$ are relatively prime, prove that $a + 2b$ and $2a+b$ are also relatively prime or have a gcd of $3$.
43591
How to factor numbers that are the product of two primes
148713
If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
68221
Question regardles primes and the fundamental theorem of arithmetic
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
7203
Prime numbers the rank of which is also a prime.
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
19979
Why does $p^2+8$ prime imply $p^3+4$ prime