If $a$ and $b$ are prime to each other and $n$ is prime then$\frac{a^n+b^n}{a+b}$ and $a+b$ have no common factor.
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
81267
A simple doubt in number theory problem.
27963
How many ways a composite number can be resolved into two factors which are prime to each other?
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
67528
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer"
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
2522
Why is $a^n - b^n$ divisible by $a-b$?
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
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 $n=3^m$.
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$