query: $24~$ divides $~p^2 -q^2$, where $~p~$ and $~q~$ are primes greater than $~5$
positive_passages.docid: 15915
positive_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 121890
negative_passages.text: Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
negative_passages.docid: 26449
negative_passages.text: $|G|=24$ prove that $G$ is not simple
negative_passages.docid: 131551
negative_passages.text: $pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
negative_passages.docid: 137808
negative_passages.text: $n^2 + 3n +5$ is not divisible by $121$
negative_passages.docid: 87282
negative_passages.text: Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
negative_passages.docid: 52032
negative_passages.text: Prove that ${n^5 - n}$ is divisible by 5
negative_passages.docid: 15191
negative_passages.text: If $a^2$ divides $b^2$, then $a$ divides $b$
negative_passages.docid: 31555
negative_passages.text: Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
negative_passages.docid: 130615
negative_passages.text: divisibility of binomial coefficients by primes
negative_passages.docid: 32803
negative_passages.text: Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
negative_passages.docid: 17965
negative_passages.text: Prove 24 divides $u^3-u$ for all odd natural numbers $u$
negative_passages.docid: 52530
negative_passages.text: There exists a prime congruent to $m$ mod $p$
negative_passages.docid: 40156
negative_passages.text: Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$
negative_passages.docid: 111967
negative_passages.text: 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 $p|y^2−y+ 25$.
negative_passages.docid: 138890
negative_passages.text: Cool property of the number $24$
negative_passages.docid: 81221
negative_passages.text: The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)