How to prove that $x=y=1$ or $x=y=−1$ if $xy=1$?
135087
Find integer solutions of $xy=-1$ (using only elementary ring theory).
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
108704
Help with proof of $|x+y| \geq |x|-|y|$
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
87665
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
63410
Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
158862
Show that $a(-1) = (-1)a = -a $.
75387
A proof that $1=2$. May I know why it’s false?
41779
Is $x/x$ equal to $1$
29679
Prove: $|x-y|\leq |x|+|y|$
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
54370
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
68092
Does square difference prove that 1 = 2?