query: $a^2+ab+b^2=1$, how many ordered integer solutions exist?
positive_passages.docid: 28594
positive_passages.text: Number of integer solutions of the following equation
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 55100
negative_passages.text: The positive integer solutions for $2^a+3^b=5^c$
negative_passages.docid: 156542
negative_passages.text: Number of solutions to $a_1 + a_2 + \dots + a_k = n$ where $n \gt 0$ and $0 \lt a_1 \leq a_2 \leq \dots \leq a_k$ are integers.
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 72857
negative_passages.text: Find the number of integral solutions of $2x + y + z = 20$?
negative_passages.docid: 33314
negative_passages.text: How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
negative_passages.docid: 69328
negative_passages.text: (USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 74827
negative_passages.text: Integer ordered pair of $(x,y)$ in complex algebraic equation
negative_passages.docid: 70662
negative_passages.text: How many non-negative integer solutions does the equation $3x + y + z = 24$ have?
negative_passages.docid: 19909
negative_passages.text: if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$
negative_passages.docid: 96185
negative_passages.text: Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
negative_passages.docid: 61022
negative_passages.text: Diophantine Equations : Solving $a^2+ b^2=2c^2$