query: How do I find integers $x,y,z$ such that $x+y=1-z$ and $x^3+y^3=1-z^2$?
positive_passages.docid: 145287
positive_passages.text: Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
negative_passages.docid: 45616
negative_passages.text: Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
negative_passages.docid: 62980
negative_passages.text: How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$?
negative_passages.docid: 157746
negative_passages.text: Finding all positive integer solutions to $(x!)(y!) = x!+y!+z!$
negative_passages.docid: 39135
negative_passages.text: Representation of integers by ternary quadratic form $x^2+y^2-z^2$
negative_passages.docid: 34393
negative_passages.text: Variation of Pythagorean triplets: $x^2+y^2 = z^3$
negative_passages.docid: 71361
negative_passages.text: Prove that $x^x+y^y=z^z$ doesn't have integer solutions
negative_passages.docid: 87994
negative_passages.text: Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$
negative_passages.docid: 77763
negative_passages.text: Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
negative_passages.docid: 88760
negative_passages.text: Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 51769
negative_passages.text: If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
negative_passages.docid: 153377
negative_passages.text: How to solve $y^2=3x^4+3x^2+1$ for integers.
negative_passages.docid: 29876
negative_passages.text: Find the number of triples $(x,y,z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 72857
negative_passages.text: Find the number of integral solutions of $2x + y + z = 20$?