query: prove that for $n\geq 8$ exist $p,q\epsilon\mathbb{N}$ so that $n=5p +3q$
positive_passages.docid: 11359
positive_passages.text: Determine the Set of a Sum of Numbers
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 105325
negative_passages.text: Expansion of $(1+px+qx^2)^8\equiv 1+8x+52x^2+kx^3$...
negative_passages.docid: 58663
negative_passages.text: How to show that if $\phi(n)$ equals to n itself, then n must be 1?
negative_passages.docid: 151928
negative_passages.text: How to prove that $N\setminus A$ is finite?
negative_passages.docid: 28266
negative_passages.text: For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
negative_passages.docid: 70926
negative_passages.text: Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
negative_passages.docid: 27147
negative_passages.text: Proving $n! > n^3$ for all $n > a$
negative_passages.docid: 40287
negative_passages.text: Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
negative_passages.docid: 139269
negative_passages.text: Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
negative_passages.docid: 51129
negative_passages.text: Proving $n^\epsilon > \log(n)$ for sufficiently large $n$
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 81124
negative_passages.text: Infinite product problem: $\sum p_n0$
negative_passages.docid: 65742
negative_passages.text: Strong Induction: Every natural number $n\geq 8$ can be represented as $n=3k + 5\ell$
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 125188
negative_passages.text: how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
negative_passages.docid: 51520
negative_passages.text: Prove that the only prime triple is 3, 5, 7