Show that $n$ is a prime number if $x,n \in\mathbb{N}>0 $ such that $1+x+x^2+x^3+...x^{n-1}$ is a prime number
136310
Prime number in a polynomial expression
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
137457
Use mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
68221
Question regardles primes and the fundamental theorem of arithmetic
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
102064
Prime number between $n$ and $n!+1$