query: If two distinct primes divides the same number, will their product divide this too?
positive_passages.docid: 24845
positive_passages.text: Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
negative_passages.docid: 119282
negative_passages.text: If $a_1,a_2,\ldots, a_n$ are distinct primes, and $a_1=2$, and $n>1$, then $a_1a_2\cdots a_n+1$ is of the form $4k+3$.
negative_passages.docid: 135682
negative_passages.text: Are distinct prime ideals in a ring always coprime? If not, then when are they?
negative_passages.docid: 21383
negative_passages.text: Can every even integer be expressed as the difference of two primes?
negative_passages.docid: 20881
negative_passages.text: Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
negative_passages.docid: 34617
negative_passages.text: Number Theory: which primes are a sum of two squares?
negative_passages.docid: 43591
negative_passages.text: How to factor numbers that are the product of two primes
negative_passages.docid: 116361
negative_passages.text: Relationship between prime factorizations of $n$ and $n+1$?
negative_passages.docid: 100984
negative_passages.text: Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
negative_passages.docid: 39698
negative_passages.text: On uniqueness of sums of prime powers
negative_passages.docid: 50413
negative_passages.text: Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
negative_passages.docid: 157456
negative_passages.text: All odd primes except $5$ divide a number made up of all $1$s
negative_passages.docid: 91935
negative_passages.text: If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
negative_passages.docid: 45700
negative_passages.text: How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime?
negative_passages.docid: 99205
negative_passages.text: Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
negative_passages.docid: 65764
negative_passages.text: Partitioning $\{1,2,\ldots,k\}$ into $p$ subsets with equal sums, where $p$ is prime
negative_passages.docid: 152231
negative_passages.text: Computing the product of p/(p - 2) over the odd primes