query: To prove $\gcd\{p^2-1: p $ is a prime $ \geq 7 \}=24$
positive_passages.docid: 15915
positive_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 14783
negative_passages.text: A Number Theory problem (GCD)
negative_passages.docid: 13317
negative_passages.text: show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
negative_passages.docid: 96062
negative_passages.text: Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
negative_passages.docid: 98544
negative_passages.text: Prove that in any GCD domain every irreducible element is prime
negative_passages.docid: 23590
negative_passages.text: Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
negative_passages.docid: 124869
negative_passages.text: Prime factor of $A=14^7+14^2+1$
negative_passages.docid: 127993
negative_passages.text: Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
negative_passages.docid: 122096
negative_passages.text: Find $GCD(n^2+1,n+1)$
negative_passages.docid: 156641
negative_passages.text: Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
negative_passages.docid: 66851
negative_passages.text: If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
negative_passages.docid: 77064
negative_passages.text: Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
negative_passages.docid: 44857
negative_passages.text: Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
negative_passages.docid: 108450
negative_passages.text: Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
negative_passages.docid: 101872
negative_passages.text: Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
negative_passages.docid: 66785
negative_passages.text: Find $\gcd(p^n-1,p^m+1)$.
negative_passages.docid: 19164
negative_passages.text: On the GCD of a Pair of Fermat Numbers