is "$a^0 = 1$" a definition or there exists a proof?
122737
How to understand why $x^0 = 1$, where $x$ is any real number?
155757
Number theory: $x^y + 1 = y^x$
145466
Is this a valid mathematical proof?
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
44596
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
53688
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
95057
Possible fake proof of $1= -1$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
60348
How do I prove $F(a)=F(a^2)?$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$