Integer solutions to $x^2(y-1)+y^2(x-1)=1$
113386
Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
135087
Find integer solutions of $xy=-1$ (using only elementary ring theory).
15753
Solve the following equation in positive integers $x$ and $y$
113268
Proving $x^4+y^4=z^2$ has no integer solutions
157746
Finding all positive integer solutions to $(x!)(y!) = x!+y!+z!$
18903
Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
10548
The equation $-1 = x^2 + y^2$ in finite fields
148570
Find the all possible real solutions of $x^y=y^x$
106271
Solutions of Diophantine equations in Natural numbers
155363
Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
158933
Rational solutions of $y^2 = x^3 - x$
106896
Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
74920
Prove that the equation $x^2-y^2 = 2002$ has no integer solution
144765
Solving $\sqrt{x+5} = x - 1$
124223
Find all pairs (x, y) of real numbers such that $16^{x^2+y} + 16^{x+y^2}=1$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$