query: Find all $(x,y)$ of positive integers s.t. $x^3-y^3=xy+61$
positive_passages.docid: 21679
positive_passages.text: Solving $x^3-y^3=xy+61$ in integers
negative_passages.docid: 114489
negative_passages.text: Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
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: 35504
negative_passages.text: The Diophantine equation $x^2 + 2 = y^3$
negative_passages.docid: 134857
negative_passages.text: Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots
negative_passages.docid: 148570
negative_passages.text: Find the all possible real solutions of $x^y=y^x$
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$
negative_passages.docid: 149254
negative_passages.text: Solving $y^3=x^3+8x^2-6x+8$
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 158124
negative_passages.text: Sum of all the positive integers problem
negative_passages.docid: 134570
negative_passages.text: Using Inclusion/Exclusion to solve $x_1+x_2+x_3=15$ with $x_1,x_2\leq 5$ and $x_3\leq 7$ for non negative integers $x_1,x_2,x_3$
negative_passages.docid: 26301
negative_passages.text: Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
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: 30261
negative_passages.text: How can I find all integers $x≠3$ such that $x−3|x^3−3$
negative_passages.docid: 41364
negative_passages.text: How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
negative_passages.docid: 8504
negative_passages.text: Factoring $x^n + y^n$ over the integers