prove that $x^2 + 5 =y^3$ has no solutions for $x,\ y \in \mathbb{Z}$
101019
$x^3-9=y^2$ find integral solutions
84893
Solutions of the equations of the degree 5 and more
82083
Solving $(z+1)^5 = z^5$
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
81854
Prove $x^4 + 131 = 3y^4$ has no integer solutions
13120
Find all integer solutions to $x^2+y^2+z^2=2xyz$
61877
Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
133164
Rational solutions for $x^2+y^2=3$
3396
Find the case when $t^3$ never equals to any of the given
88189
Finding all integer solutions of $5^x+7^y=2^z$
9542
Integer solutions for $x^2-y^3 = 23$.
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
147952
Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
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
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers