Prove that: $x^2+y^2+z^2=2xyz$ has no answer over $\Bbb{N}$
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
106374
Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
147952
Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
20964
Proof that $n^2 < 2^n$
125604
Proof that $\mathbb{Z}$ has no zero divisors
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
54370
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
108244
Proof without solving equation that if $(1+z)^n = (1-z)^n$ then Re(z) = 0. Did I do it right?
111467
find all natural solution that satisfy $x^2+y^2 = 3z^2$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
146241
If $a \in \Bbb Z$ is the sum of two squares then $a$ can't be written in which of the following forms?
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$