query: Find all $z$ such that $(z+1)^7 = z^7$. You do not have to put your answer in the simplest rectangular or exponential form.
positive_passages.docid: 24822
positive_passages.text: How to solve the equation $(z+1)^7 = z^7$ for all $z$?
negative_passages.docid: 133863
negative_passages.text: All pairs (x,y) that satisfy the equation $xy+(x^3+y^3)/3=2007$
negative_passages.docid: 155363
negative_passages.text: Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
negative_passages.docid: 61987
negative_passages.text: $x^2+1=0$ in $\mathbb{Z}_7$
negative_passages.docid: 88189
negative_passages.text: Finding all integer solutions of $5^x+7^y=2^z$
negative_passages.docid: 65280
negative_passages.text: If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
negative_passages.docid: 90786
negative_passages.text: What are $x$, $y$ and $z$ if $\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y} = 4$ and $x$, $y$ and $z$ are whole numbers?
negative_passages.docid: 38568
negative_passages.text: Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
negative_passages.docid: 23901
negative_passages.text: Find every $z$s that fit $\cos(z) = -2$
negative_passages.docid: 86935
negative_passages.text: Finding all the numbers that fit $x! + y! = z!$
negative_passages.docid: 111295
negative_passages.text: Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
negative_passages.docid: 85917
negative_passages.text: Solve $(x+1)^y-x^z=1$
negative_passages.docid: 40447
negative_passages.text: Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.
negative_passages.docid: 84283
negative_passages.text: If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$.
negative_passages.docid: 123159
negative_passages.text: Solutions of the diophantine equation $x+y+z=xyz$?
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 7491
negative_passages.text: How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?