Proving that $y^2=x^3-6$ has no integer solutions
50760
Solutions to $y^2 = x^3 + k$?
71756
diophantine equation: $x^2 +y^2 = z^n$
84379
Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289
113268
Proving $x^4+y^4=z^2$ has no integer solutions
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
22112
Find all integer solutions to $x^2+4=y^3$.
52857
Behaviour of $\frac{x^{3} y}{x^{6} + y^{2}}$ around origin
44744
Integer solutions of $xy+9(x+y)=2006$
59653
$x^2-y^2=2s$, s cannot be an odd integer
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
24322
Prove that the equation $18x+42y=22$ has no integer solution?
119152
Proving irreducibility of $x^6-72$
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.