Show that $x^2 + y^2 = z^n$ has positive integer solutions for $n = 1,2,3,...$
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
111467
find all natural solution that satisfy $x^2+y^2 = 3z^2$
144863
Finding integer solutions to $y^2=x^3-2$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
62036
Finding the number of non-negative integral solutions of $x + y + z = 10$
20964
Proof that $n^2 < 2^n$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
39993
Count the number of positive solutions for a linear diophantine equation
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
157746
Finding all positive integer solutions to $(x!)(y!) = x!+y!+z!$
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
94700
Integer solutions for $x^3+2=y^2$?
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers