query: Largest integer such that $n+5$ divides $n^3+89$
positive_passages.docid: 62043
positive_passages.text: the largest integer $n$ for which $n+5$ divivides $n^5+5$?
negative_passages.docid: 78416
negative_passages.text: Show that $7$ divides $a^{15}-a^3$ for any integer $a$
negative_passages.docid: 126889
negative_passages.text: Proof by induction: inequality $n! > n^3$ for $n > 5$
negative_passages.docid: 58418
negative_passages.text: Does there exist a set of exactly five positive integers such that the sum of any three distinct elements is prime?
negative_passages.docid: 95141
negative_passages.text: $n^5-n$ is divisible by $10$?
negative_passages.docid: 52032
negative_passages.text: Prove that ${n^5 - n}$ is divisible by 5
negative_passages.docid: 29764
negative_passages.text: Find the largest of the three prime divisors of the number $13^4 + 16^5 - 172^2$
negative_passages.docid: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 10589
negative_passages.text: How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
negative_passages.docid: 18693
negative_passages.text: If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
negative_passages.docid: 110722
negative_passages.text: $n$ and $n^5$ have the same units digit?
negative_passages.docid: 49096
negative_passages.text: How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
negative_passages.docid: 150185
negative_passages.text: Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$
negative_passages.docid: 98443
negative_passages.text: Find positive integers such that $2n^3 + 5|n^4 +n+1$
negative_passages.docid: 120227
negative_passages.text: Proving $6^n - 1$ is always divisible by $5$ by induction
negative_passages.docid: 32653
negative_passages.text: Smallest integer divisible by all up to $n$
negative_passages.docid: 112191
negative_passages.text: How can I show $q^k$ does not divide ${{n}\choose{q}}$ when $q$ is a prime factor of $n$ and $k$ is the largest integer such that $q^k$ divides $n$?