query: Finding integer solutions of $ 2^{m} + 1 = 3^{n} $.
positive_passages.docid: 7279
positive_passages.text: $|2^x-3^y|=1$ has only three natural pairs as solutions
negative_passages.docid: 22112
negative_passages.text: Find all integer solutions to $x^2+4=y^3$.
negative_passages.docid: 61877
negative_passages.text: Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$
negative_passages.docid: 59091
negative_passages.text: A quartic diophantine equation
negative_passages.docid: 21874
negative_passages.text: Solve $x^3+x \equiv 1 \pmod p$
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 21679
negative_passages.text: Solving $x^3-y^3=xy+61$ in integers
negative_passages.docid: 153170
negative_passages.text: Find the number of solutions of the equation $e^{4x}+e^{3x}-4e^{2x}+e^x+1=0$
negative_passages.docid: 54929
negative_passages.text: Finding integer solutions for $6x+15y+20z=1$
negative_passages.docid: 50772
negative_passages.text: Solving a Linear Diophantine Equation
negative_passages.docid: 107448
negative_passages.text: proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
negative_passages.docid: 77024
negative_passages.text: Find the number of solutions of $x^2=x\mod m$ for any integer $m$
negative_passages.docid: 20834
negative_passages.text: Integer solutions to $c=a^2-b^2$
negative_passages.docid: 8446
negative_passages.text: Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$
negative_passages.docid: 53042
negative_passages.text: Find solutions to $\varphi\left(n\right)=2^{32}$
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 103832
negative_passages.text: Number of solutions of $x_1 + x_2 + x_3 + x_4 = 14$ such that $x_i \le 6$