Given $a+b+..=a^7+b^7+..=0$ show that $a(a+b)..=0$
27637
How can I apply Newton's sums to solve this problem?
145125
How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
27387
Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
77212
Show that for any real constants a and b, where b > 0, (n + a) b = Θ(n b ).
61987
$x^2+1=0$ in $\mathbb{Z}_7$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
89279
If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
149287
Prove that $A,B>0$ and $A_{ij}0$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
118467
Prove that $a^2+ab+b^2\ge 0$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
73570
Sum of (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on)