query: Diophantine equation of $a^2+b^2=c^2+d^2$
positive_passages.docid: 18203
positive_passages.text: Diophantine equation $a^2+b^2=c^2+d^2$
negative_passages.docid: 5729
negative_passages.text: If $a^2+b^2+c^2=1$ then prove the following.
negative_passages.docid: 155012
negative_passages.text: Solving quadratic equations in modular arithmetic
negative_passages.docid: 6621
negative_passages.text: Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
negative_passages.docid: 71756
negative_passages.text: diophantine equation: $x^2 +y^2 = z^n$
negative_passages.docid: 132098
negative_passages.text: Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
negative_passages.docid: 1001
negative_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 4333
negative_passages.text: Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
negative_passages.docid: 147562
negative_passages.text: Sum of squares diophantine equation
negative_passages.docid: 73160
negative_passages.text: Solving the Diophantine Equation $x^2 - y! = 2001$ and $x^2 - y! = 2016$
negative_passages.docid: 118467
negative_passages.text: Prove that $a^2+ab+b^2\ge 0$
negative_passages.docid: 96185
negative_passages.text: Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 103165
negative_passages.text: the number of the positive integer numbers $k$ that makes for the two quadratic equations $ \pm x^2 \pm px \pm k$ rational roots.
negative_passages.docid: 8276
negative_passages.text: How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?
negative_passages.docid: 147442
negative_passages.text: Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
negative_passages.docid: 6777
negative_passages.text: Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$