query: Find the positive integral values $n$ can take :${(x+y+z)}^2=nxyz$
positive_passages.docid: 29151
positive_passages.text: Equation with Vieta Jumping: $(x+y+z)^2=nxyz$.
negative_passages.docid: 155559
negative_passages.text: Quickest way to determine a polynomial with positive integer coefficients
negative_passages.docid: 13120
negative_passages.text: Find all integer solutions to $x^2+y^2+z^2=2xyz$
negative_passages.docid: 88760
negative_passages.text: Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$
negative_passages.docid: 18313
negative_passages.text: show this inequality with $xy+yz+zx=3$
negative_passages.docid: 120213
negative_passages.text: Example $x$, $y$ and $z$ values for $x\uparrow^\alpha y=z$ where $\alpha\in \Bbb R-\Bbb N$
negative_passages.docid: 7466
negative_passages.text: How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
negative_passages.docid: 103555
negative_passages.text: Find all positive integral soludions of $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 4$
negative_passages.docid: 47809
negative_passages.text: If $x,y\in\mathbb Z$, solve $x^2+xy+y^2=x^2y^2$.
negative_passages.docid: 102636
negative_passages.text: Contour Integral: $\int^{\infty}_{0}(1+z^n)^{-1}dz$
negative_passages.docid: 118197
negative_passages.text: Solve $n(n+1)(n+2)=6m^3$ in positive integers
negative_passages.docid: 87338
negative_passages.text: Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$
negative_passages.docid: 146126
negative_passages.text: Infinite positive integer solutions of the equation: $x^2+x+1=(y^2+y+1)(n^2+n+1)$
negative_passages.docid: 27911
negative_passages.text: How can I prove that $xy\leq x^2+y^2$?
negative_passages.docid: 106729
negative_passages.text: Least Value Of $x+y+z$
negative_passages.docid: 16820
negative_passages.text: Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle
negative_passages.docid: 87345
negative_passages.text: How many ways so that $x+y+z\leq n$?