If $B ∈ M_n(F)$ such that AB = BA, prove that $B = a_0 + a_1A + a_2A^2 + ··· +a_{n−1}A^{n−1 }$
108850
Complex matrix that commutes with another complex matrix.
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
136367
Prove $ ∀a, b, c ∈ Z,$ if $ab + ac ≡ 3$ (mod 6) then b $\not\equiv$ c (mod 6).
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
43010
Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
127296
prove that a|b and b|a iff a=+-b
109498
Linear maps $f: M_n \longrightarrow \mathbb{R}$ such that $f(AB) = f(BA)$
96630
Let a and b be real numbers such that 0  \sqrt{ab} > \frac{2ab}{a + b}$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.