query: Express $x^4 + y^4 + x^2 + y^2$ as sum of squares of three polynomials in $x,y$
positive_passages.docid: 148834
positive_passages.text: Find three polynomials whose squares sum up to $x^4 + y^4 + x^2 + y^2$
negative_passages.docid: 138756
negative_passages.text: How to Calculate the Sum of Coefficients in a Polynomial with known Integer Roots
negative_passages.docid: 143194
negative_passages.text: How would you solve the diophantine $x^4+y^4=2z^2$
negative_passages.docid: 86285
negative_passages.text: Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
negative_passages.docid: 15403
negative_passages.text: Sum of square of function
negative_passages.docid: 39135
negative_passages.text: Representation of integers by ternary quadratic form $x^2+y^2-z^2$
negative_passages.docid: 125274
negative_passages.text: For $x+y=1$, show that $x^4+y^4\ge \frac{1}{8}$
negative_passages.docid: 53725
negative_passages.text: Factor $(x+y)^4+x^4+y^4$
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 1379
negative_passages.text: Summation of $n^2x^n$ terms
negative_passages.docid: 44296
negative_passages.text: Solving a cubic polynomial equation.
negative_passages.docid: 149254
negative_passages.text: Solving $y^3=x^3+8x^2-6x+8$
negative_passages.docid: 137015
negative_passages.text: Solutions for $a^2+b^2+c^2=d^2$
negative_passages.docid: 129646
negative_passages.text: Defining a function that completes the square given a quadratic polynomial expression
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$
negative_passages.docid: 111467
negative_passages.text: find all natural solution that satisfy $x^2+y^2 = 3z^2$
negative_passages.docid: 38705
negative_passages.text: Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$