query: Prove: if $x$ is even, then $x + 5$ is odd.
positive_passages.docid: 18953
positive_passages.text: Prove that even + odd is odd.
negative_passages.docid: 13914
negative_passages.text: If $a^2+b^2=c^2$ then $a$ or $b$ is even.
negative_passages.docid: 92057
negative_passages.text: Prove that for every odd integer n, there is a group...
negative_passages.docid: 44182
negative_passages.text: Proving that an integer is even if and only if it is not odd
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 107105
negative_passages.text: Is an irrational number odd or even?
negative_passages.docid: 153532
negative_passages.text: Proving $a^2$ is even $\implies$ $a$ is even by contradiction
negative_passages.docid: 24160
negative_passages.text: Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
negative_passages.docid: 140294
negative_passages.text: prove that $n >2$ and $n$ is a prime then $n$ is odd
negative_passages.docid: 137970
negative_passages.text: $2 + 2 = 5$ (Fake proof, or ?)
negative_passages.docid: 156266
negative_passages.text: Solving $|x-2| + |x-5|=3$
negative_passages.docid: 127848
negative_passages.text: Determine which Fibonacci numbers are even
negative_passages.docid: 41418
negative_passages.text: $2+2 = 5$? error in proof
negative_passages.docid: 129680
negative_passages.text: Prove that $n$ is even.
negative_passages.docid: 5914
negative_passages.text: Proving $\lfloor 2x \rfloor = \lfloor x \rfloor + \lfloor x+0.5\rfloor$
negative_passages.docid: 79219
negative_passages.text: Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
negative_passages.docid: 94389
negative_passages.text: Proving formula for product of first n odd numbers