Show if $f_1|_{\mathbb Q} = f_2|_{\mathbb Q}$ then $f_1 = f_2$
2321
Can there be two distinct, continuous functions that are equal at all rationals?
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
95379
Prove that $V = V_1 \oplus V_2$ in the following
62615
If F is a finite field, then $F^F=P_F$.
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
15626
Relations of a~b iff b = ak^2
35959
irreducibility of a polynomial over $\mathbb{F}_2$
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$