query: Show that $p^2 = 1\pmod {24}$
positive_passages.docid: 15915
positive_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 100361
negative_passages.text: Show that ord$_{p}2 = 2^{n + 1}$.
negative_passages.docid: 152039
negative_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 128566
negative_passages.text: Proving $2$ generates $(\mathbb{Z}/19\mathbb{Z})^*$ by only looking at a few powers
negative_passages.docid: 29640
negative_passages.text: If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
negative_passages.docid: 158863
negative_passages.text: How to prove $\sum_p p^{-2} < \frac{1}{2}$?
negative_passages.docid: 4970
negative_passages.text: For $n \geq 2$, show that $n \nmid 2^{n}-1$
negative_passages.docid: 54286
negative_passages.text: Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
negative_passages.docid: 5978
negative_passages.text: Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
negative_passages.docid: 109532
negative_passages.text: Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
negative_passages.docid: 147101
negative_passages.text: Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
negative_passages.docid: 12210
negative_passages.text: Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
negative_passages.docid: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 22962
negative_passages.text: How to show $\binom{2p}{p} \equiv 2\pmod p$?
negative_passages.docid: 86594
negative_passages.text: If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
negative_passages.docid: 108237
negative_passages.text: Show $a^p \equiv b^p \mod p^2$
negative_passages.docid: 92700
negative_passages.text: How can I solve $x^2 \equiv 19 \pmod {59}$.