Prove: Let 𝑥 ∈ ℤ and 𝑝, 𝑞 be distinct primes. Then p|x and q|x if and only if pq|x
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
130731
Is every integer the sum of distinct prime numbers?
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
135586
Prove that the preimage of a prime ideal is also prime.
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
87624
If $\mathrm{char}(K)=p$ is prime, $L/K$ is separable if and only if $K(\alpha) =K(\alpha^p)$ for all $\alpha \in L$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
83173
Prove linear combinations of logarithms of primes over $\mathbb{Q}$ is independent
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.