query: Show that if $p=2^a -1 $ is prime then a is prime
positive_passages.docid: 143772
positive_passages.text: How can I algebraically prove that $2^n - 1$ is not always prime?
negative_passages.docid: 72672
negative_passages.text: Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
negative_passages.docid: 70066
negative_passages.text: Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
negative_passages.docid: 21629
negative_passages.text: Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
negative_passages.docid: 5841
negative_passages.text: Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
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
negative_passages.docid: 39915
negative_passages.text: Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
negative_passages.docid: 51382
negative_passages.text: Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
negative_passages.docid: 102889
negative_passages.text: If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
negative_passages.docid: 130846
negative_passages.text: Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
negative_passages.docid: 140830
negative_passages.text: Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
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: 101057
negative_passages.text: Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
negative_passages.docid: 108380
negative_passages.text: Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
negative_passages.docid: 126945
negative_passages.text: checking if a number is a prime
negative_passages.docid: 100426
negative_passages.text: Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
negative_passages.docid: 63356
negative_passages.text: Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?