query: Prove $x + y$ is divisible by $11$. Is my solution correct?
positive_passages.docid: 145889
positive_passages.text: Prove if $56x = 65y$ then $x + y$ is divisible by $11$
negative_passages.docid: 85959
negative_passages.text: How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
negative_passages.docid: 122711
negative_passages.text: Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
negative_passages.docid: 106981
negative_passages.text: Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
negative_passages.docid: 34784
negative_passages.text: Is a number meeting these conditions divisible by forty-nine?
negative_passages.docid: 79940
negative_passages.text: $\binom{p}{i}$ divisible by $p$, with $p$ prime
negative_passages.docid: 12729
negative_passages.text: Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
negative_passages.docid: 35666
negative_passages.text: How to prove the divisibility rule for $3\, $ [casting out threes]
negative_passages.docid: 49501
negative_passages.text: Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
negative_passages.docid: 82742
negative_passages.text: Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
negative_passages.docid: 48908
negative_passages.text: Choose 100 numbers from 1~200 (one less than 16) - prove one is divisible by another!
negative_passages.docid: 8366
negative_passages.text: Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
negative_passages.docid: 155757
negative_passages.text: Number theory: $x^y + 1 = y^x$
negative_passages.docid: 153892
negative_passages.text: Number Theory divisibilty
negative_passages.docid: 142724
negative_passages.text: Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
negative_passages.docid: 127183
negative_passages.text: Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
negative_passages.docid: 59135
negative_passages.text: What is the proof of divisibility by $13$?