query: Solve the Diophantine equations: $|a^2 -2b^2|=1$?
positive_passages.docid: 86807
positive_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 56803
negative_passages.text: Finding solutions to congruence equations
negative_passages.docid: 99739
negative_passages.text: The diophantine equation $x^2+y^2=3z^2$
negative_passages.docid: 155659
negative_passages.text: Is there a formula for solving the congruence equation $ax^2 + bx + c=0$?
negative_passages.docid: 10635
negative_passages.text: diophantine equations $x^3-2y^3=1$
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 108035
negative_passages.text: solving diophantine equations using congruences
negative_passages.docid: 58589
negative_passages.text: On the factorial equations $A! B! =C!$ and $A!B!C! = D!$
negative_passages.docid: 41890
negative_passages.text: How to get all solutions of $x^2 \equiv$ $a$ mod $p$?
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 18053
negative_passages.text: Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
negative_passages.docid: 123441
negative_passages.text: Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 72463
negative_passages.text: How to solve a quartic equation?
negative_passages.docid: 156468
negative_passages.text: Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?