How prove this $4A^5+2A^3+A=7I$
31186
Hermitian matrix such that $4M^5+2M^3+M=7I_n$
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
50777
Prove that $4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$ .
63505
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
127400
Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5
89804
Diophantine equation: $7^x=3^y-2$
15985
simplify $(a_1 + a_2 +a_3+... +a_n)^m$
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
100450
Prove that 3 is a primitive root of $7^k$ for all $k \ge 1$
19940
How to show that $A^3+B^3+C^3 - 3ABC = (A+B+C)(A+B\omega+C\omega^2)(A+B\omega^2+C\omega)$ indirectly?
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
126018
Show that $ e^{A+B}=e^A e^B$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
89184
Prove $30|(a^3b-ab^3) $
104658
proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$