query: Prove that $n^{34}-9$ is never prime for any $n$.
positive_passages.docid: 25428
positive_passages.text: Prime numbers of the form $ n^{34} -9$
negative_passages.docid: 82485
negative_passages.text: Show that the set of non zero rationals is not a cyclic group under multiplication.
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 140405
negative_passages.text: Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
negative_passages.docid: 28099
negative_passages.text: Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
negative_passages.docid: 71110
negative_passages.text: Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
negative_passages.docid: 45911
negative_passages.text: Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
negative_passages.docid: 95240
negative_passages.text: Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
negative_passages.docid: 24444
negative_passages.text: Prove that $371\cdots 1$ is not prime
negative_passages.docid: 59261
negative_passages.text: If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.
negative_passages.docid: 77240
negative_passages.text: Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
negative_passages.docid: 46102
negative_passages.text: Prove that $2^n +1$ in never a perfect cube
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 114810
negative_passages.text: $n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
negative_passages.docid: 131289
negative_passages.text: Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
negative_passages.docid: 107725
negative_passages.text: Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
negative_passages.docid: 21862
negative_passages.text: Proof of lack of pure prime producing polynomials.