query: How to find all integer pairs $(x,y)$ that satisfy the equation $21x+47y=1$ without using modular arithmetic?
positive_passages.docid: 24322
positive_passages.text: Prove that the equation $18x+42y=22$ has no integer solution?
negative_passages.docid: 9542
negative_passages.text: Integer solutions for $x^2-y^3 = 23$.
negative_passages.docid: 35066
negative_passages.text: Nature and number of solutions to $xy=x+y$
negative_passages.docid: 9039
negative_passages.text: What is the best way to solve modular arithmetic equations such as $9x \equiv 33 \pmod{43}$?
negative_passages.docid: 48949
negative_passages.text: Solving a Diophantine equation with a large solution
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 145617
negative_passages.text: Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?
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: 82931
negative_passages.text: How do I solve a linear Diophantine equation with three unknowns?
negative_passages.docid: 22112
negative_passages.text: Find all integer solutions to $x^2+4=y^3$.
negative_passages.docid: 146126
negative_passages.text: Infinite positive integer solutions of the equation: $x^2+x+1=(y^2+y+1)(n^2+n+1)$
negative_passages.docid: 105347
negative_passages.text: How many nonnegative integer solutions are there to the pair of equations $x_1+x_2+…+x_6=20$ and $x_1+x_2+x_3=7$?
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: 104966
negative_passages.text: Find integer solution to the given system of equation.
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 131941
negative_passages.text: Solve quadratic congruences.
negative_passages.docid: 30045
negative_passages.text: Solving linear congruences by hand: modular fractions and inverses