$x^3 - 6 = 25y^2 + 35y$ has no non-zero integer solutions
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
44744
Integer solutions of $xy+9(x+y)=2006$
12150
For what value of m that the equation $y^2 = x^3 + m$ has no integral solutions?
69874
Are there any integer solutions to $a^3=b^2$?
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
106374
Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
25518
How can I solve the equation $x^3-x-1 = 0$?
133680
On the equation $3x^3 + 4y^3 + 5z^3 = 0$
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
114954
Solve the equation $x^3 + 117y^3 = 5$ over the integers.
50760
Solutions to $y^2 = x^3 + k$?
16400
Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution.
149254
Solving $y^3=x^3+8x^2-6x+8$
24322
Prove that the equation $18x+42y=22$ has no integer solution?
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
70662
How many non-negative integer solutions does the equation $3x + y + z = 24$ have?