$x+y=2$ implies $x^3y^3(x^3+y^3)≤2$, for positive $x$ and $y$.
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
7775
Show that $|x-y|\leq |x|+|y|$.
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
50433
Prove $4(x + y + z)^3 > 27(x^2y + y^2z + z^2x)$
22004
Inverse of $y = x^3 + x $?
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
108704
Help with proof of $|x+y| \geq |x|-|y|$
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
35504
The Diophantine equation $x^2 + 2 = y^3$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$