query: Diophantine equation $x^2+y^2+1=xyz$
positive_passages.docid: 25784
positive_passages.text: Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.
negative_passages.docid: 78719
negative_passages.text: Solve the DE $yy^{\prime}+x=\sqrt{x^2+y^2}$
negative_passages.docid: 946
negative_passages.text: How to find solutions of linear Diophantine ax + by = c?
negative_passages.docid: 143194
negative_passages.text: How would you solve the diophantine $x^4+y^4=2z^2$
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 108035
negative_passages.text: solving diophantine equations using congruences
negative_passages.docid: 12837
negative_passages.text: Inequality with condition $x^2+y^2+z^2=1$.
negative_passages.docid: 111443
negative_passages.text: Optimization of $2x+3y+z$ under the constraint $x^2+ y^2+ z^2= 1$
negative_passages.docid: 29151
negative_passages.text: Equation with Vieta Jumping: $(x+y+z)^2=nxyz$.
negative_passages.docid: 71361
negative_passages.text: Prove that $x^x+y^y=z^z$ doesn't have integer solutions
negative_passages.docid: 113386
negative_passages.text: Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 72023
negative_passages.text: Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
negative_passages.docid: 105302
negative_passages.text: Solutions of bivariate cubic Diophantine equation
negative_passages.docid: 61877
negative_passages.text: Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$