Show that if n is odd, then the equation $x^2-y^2=2n$ has no integer solutions x,y.
59653
$x^2-y^2=2s$, s cannot be an odd integer
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
32771
The equation $X^{n} + Y^{n} = Z^{n}$ , where $ n \geq 3$ is a natural number, has no solutions at all where $X,Y,Z$ are intergers.
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
103784
Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
35504
The Diophantine equation $x^2 + 2 = y^3$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
96185
Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
6453
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
12150
For what value of m that the equation $y^2 = x^3 + m$ has no integral solutions?
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
71756
diophantine equation: $x^2 +y^2 = z^n$