Show that if $x^n=y^n$ and $n$ is odd, then $x=y$
97411
If $x^n=y^n$ and $n$ is odd then $x=y$
18633
Prove every odd integer is the difference of two squares
135614
Show that $2^n > n^2$ whenever n>4.
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
74835
how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
40269
Proving if $x^3$ is even, then $x$ is even.
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
134000
Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
103504
Weird $3^n$ in an identity to be combinatorially proved
155757
Number theory: $x^y + 1 = y^x$