query: Find infinitely many integral solutions $(x^2+x+1)(y^2+y+1)=z^2 +z+1 $
positive_passages.docid: 146126
positive_passages.text: Infinite positive integer solutions of the equation: $x^2+x+1=(y^2+y+1)(n^2+n+1)$
negative_passages.docid: 79925
negative_passages.text: Infinitely many values of $x$ that satisfy the equations
negative_passages.docid: 38541
negative_passages.text: How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$?
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 57330
negative_passages.text: Find the number of solutions of $\sin x+2 \sin 2x- \sin 3x=3$
negative_passages.docid: 45616
negative_passages.text: Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
negative_passages.docid: 124223
negative_passages.text: Find all pairs (x, y) of real numbers such that $16^{x^2+y} + 16^{x+y^2}=1$
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$
negative_passages.docid: 20034
negative_passages.text: Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
negative_passages.docid: 18903
negative_passages.text: Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
negative_passages.docid: 66317
negative_passages.text: How to solve $z^3+z+1=0$?
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$
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: 139930
negative_passages.text: Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
negative_passages.docid: 95494
negative_passages.text: Number of solutions of an arithmetic function's equation
negative_passages.docid: 70406
negative_passages.text: Find all values x, y and z which satisfy the equation $(x^2 + 1)(y^2 + 1) = z^2 + 1$ given that $(x^2 + 1)$ and $(y^2 + 1)$ are both primes.