If $A \in M_5(\mathbb R)$ and $A^2-4A-I=0$ find $(a_1-\frac{1}{a_1})+\ldots+(a_5-\frac{1}{a_5})$
124583
A question about eigenvalues of $5\times5$ matrix
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
28861
Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
95036
For any integer $a$, $\gcd(11a+5,2a+1)=1$.
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
140342
$\frac {1}{5}-\frac{1.4}{5.10}+\frac{1.4.7}{5.10.15}-\cdot\cdot\cdot\cdot\cdot\cdot\cdot$
144765
Solving $\sqrt{x+5} = x - 1$
95669
Solutions of $|z| = z^5$ in $\Bbb{C}$?
2300
Determine the remainder when $f(x) = 3x^5 - 5x^2 + 4x + 1$ is divided by $(x-1)(x+2)$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
15268
Find all $x,y \in \mathbb N^*$ such that $\frac{1}{x} + \frac{1}{y}=5$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$