Prove that the sum and product of two positive relatively prime integers are themselves relatively prime.
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
108688
An identity involving products of sums
27250
Greatest common divisor of two relatively primes
113391
Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too.
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
120309
Number Theory Inequality Proof
137457
Use mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
82071
divisor of a product of integers is a product of divisors
54554
If a product of relatively prime integers is an $n$th power, then each is an $n$th power
29692
Proof verification: elementary Number Theory Proof of $am+bn = 1$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
77070
Prove Euler's Theorem when the integers are not relatively prime
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$