For all natural numbers $x$ and $y$ if $S(x)=S(y)$ then $x=y$.
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
109159
What's the intuition behind $(\exists y)(\mathscr{C}(y)\supset\mathscr{D})\supset((\forall x)\mathscr{C}(x)\supset\mathscr{D})$
142313
Find all natural numbers $x,y$ such that $3^x=2y^2+1$.
145873
Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
35066
Nature and number of solutions to $xy=x+y$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
104987
Equivalence Relation with dividing x and y integers
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
49994
Deduction of $\forall y \exists x (x=y)$
146665
Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
135926
Either X(s) or Y(s) is/are
113329
Let $S=\{1,2,3,4,\dotsc,N\}$ and $X=\{ f: S \rightarrow S \mid x < y \Rightarrow f(x)\leqslant f(y)\}$. Then $|X|$ is equal to what?
76884
Are $X$ and $X+Y$ independent, if $X$ and $Y$ are independent?
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
96341
Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers.
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$