query: Solution to the Diophantine equation $x^4+y^4=2z^2$
positive_passages.docid: 143194
positive_passages.text: How would you solve the diophantine $x^4+y^4=2z^2$
negative_passages.docid: 55206
negative_passages.text: Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 139051
negative_passages.text: Pell type equation: $x^2-py^2=a$
negative_passages.docid: 145287
negative_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: 114489
negative_passages.text: Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
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: 129454
negative_passages.text: Solution to a quadratic form
negative_passages.docid: 52658
negative_passages.text: What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 94327
negative_passages.text: Cubic Diophantine with two variables
negative_passages.docid: 153377
negative_passages.text: How to solve $y^2=3x^4+3x^2+1$ for integers.
negative_passages.docid: 72023
negative_passages.text: Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$
negative_passages.docid: 128576
negative_passages.text: How to find $x^4+y^4+z^4$ from equation?
negative_passages.docid: 56803
negative_passages.text: Finding solutions to congruence equations