Proving $\rm{card}(\Bbb Z)=\rm{card}(\Bbb N)$
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
129304
Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
59885
Proof Verification - Every sequence in $\Bbb R$ contains a monotone sub-sequence
32772
Proving units in a ring
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
104855
Prove that $N \subset Z(G)$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.