query: Prove that $24|p^2-q^2$ where $p $ and $ q$ are primes $p>q>5$
positive_passages.docid: 10425
positive_passages.text: Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
negative_passages.docid: 64782
negative_passages.text: How to prove if $n$ is prime and $n | a^2$ then $n | a$?
negative_passages.docid: 126893
negative_passages.text: A group of order 2p (p prime) and other conditions - prove abelian.
negative_passages.docid: 60804
negative_passages.text: About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
negative_passages.docid: 144575
negative_passages.text: Factoring n, where n=pq and p and q are consecutive primes
negative_passages.docid: 147777
negative_passages.text: If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
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: 140294
negative_passages.text: prove that $n >2$ and $n$ is a prime then $n$ is odd
negative_passages.docid: 23684
negative_passages.text: Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
negative_passages.docid: 37093
negative_passages.text: If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
negative_passages.docid: 75378
negative_passages.text: how to prove this extended prime number theorem?
negative_passages.docid: 51445
negative_passages.text: Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$
negative_passages.docid: 118574
negative_passages.text: prove that $24 \mid a(a^2-1)$
negative_passages.docid: 73515
negative_passages.text: Primes Number Theory
negative_passages.docid: 70066
negative_passages.text: Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
negative_passages.docid: 83407
negative_passages.text: How to show that that $q \mid p-1$?
negative_passages.docid: 144622
negative_passages.text: Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime