query: If $2^{2k}-x^2\bigm|2^{2k}-1$ then $x=1$
positive_passages.docid: 148647
positive_passages.text: If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 26514
negative_passages.text: Prove that if $n$ is a composite, then $2^n-1$ is composite.
negative_passages.docid: 97196
negative_passages.text: $k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
negative_passages.docid: 41779
negative_passages.text: Is $x/x$ equal to $1$
negative_passages.docid: 62485
negative_passages.text: How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
negative_passages.docid: 75387
negative_passages.text: A proof that $1=2$. May I know why it’s false?
negative_passages.docid: 44897
negative_passages.text: Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
negative_passages.docid: 15191
negative_passages.text: If $a^2$ divides $b^2$, then $a$ divides $b$
negative_passages.docid: 155757
negative_passages.text: Number theory: $x^y + 1 = y^x$
negative_passages.docid: 79274
negative_passages.text: $1=2$ | Continued fraction fallacy
negative_passages.docid: 111505
negative_passages.text: Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 74222
negative_passages.text: If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
negative_passages.docid: 151806
negative_passages.text: Prove that $A^k = 0 $ iff $A^2 = 0$
negative_passages.docid: 36083
negative_passages.text: If $k > 1$, then $\frac1{(k - 1)^2}-\frac1{(k + 1)^2}=\frac{4k}{(k^2 - 1)^2}$, hence simplify $\sum\limits_{k = 2}^n\frac k{(k^2 - 1)^2}$