Prove that if $A \sim I_n$ and $A \sim I_m$ then $n=m$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
72256
Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
33741
If $A\simeq\prod A_i$ then $\sum e_i=1$
129680
Prove that $n$ is even.
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
149287
Prove that $A,B>0$ and $A_{ij}0$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
75614
Proving that $n|m\implies f_n|f_m$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?