query: Do there exist whole number solutions to $27y + 23 = 32x$ and $81y + 85 = 128x$?
positive_passages.docid: 946
positive_passages.text: How to find solutions of linear Diophantine ax + by = c?
negative_passages.docid: 135742
negative_passages.text: Solve system of simultaneous equations in $3$ variables: $x+y+xy=19$, $y+z+yz=11$, $z+x+zx=14$
negative_passages.docid: 62446
negative_passages.text: Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$
negative_passages.docid: 68960
negative_passages.text: How to solve $ 13x \equiv 1 ~ (\text{mod} ~ 17) $?
negative_passages.docid: 120736
negative_passages.text: If xy + yz + zx = 1, ...........
negative_passages.docid: 30126
negative_passages.text: Linear Diophantine Equations in Three Variables
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the 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: 38811
negative_passages.text: Solutions to $\frac1{\lfloor x\rfloor}+\frac1{\lfloor 2x\rfloor}=\{x\}+\frac13$
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 114996
negative_passages.text: $x+y+z=n$. Finding the number of solutions.
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 65246
negative_passages.text: Algebraic process to find numbers so that $xy=45$ and $x+y=18$
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: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 88189
negative_passages.text: Finding all integer solutions of $5^x+7^y=2^z$