query: Find all solutions to the diophantine equation $7^x=3^y+4$ in positive integers.
positive_passages.docid: 26692
positive_passages.text: Equation in integers $7^x-3^y=4$
negative_passages.docid: 103993
negative_passages.text: Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
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: 946
negative_passages.text: How to find solutions of linear Diophantine ax + by = c?
negative_passages.docid: 128107
negative_passages.text: find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
negative_passages.docid: 62688
negative_passages.text: Find all real solutions to the equation$4^x+6^{x^2}=5^x+5^{x^2}$
negative_passages.docid: 18203
negative_passages.text: Diophantine equation $a^2+b^2=c^2+d^2$
negative_passages.docid: 71756
negative_passages.text: diophantine equation: $x^2 +y^2 = z^n$
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: 105302
negative_passages.text: Solutions of bivariate cubic Diophantine equation
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: 47001
negative_passages.text: Cubic diophantine equation
negative_passages.docid: 65000
negative_passages.text: prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
negative_passages.docid: 23835
negative_passages.text: Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
negative_passages.docid: 59091
negative_passages.text: A quartic diophantine equation
negative_passages.docid: 103020
negative_passages.text: Find all integral solutions of $ x^4 + y^4 + z^4 -w^4 = 1995 $
negative_passages.docid: 133863
negative_passages.text: All pairs (x,y) that satisfy the equation $xy+(x^3+y^3)/3=2007$