Showing that $2^{50}<3^{33}$
57041
How would you prove that $2^{50} < 3^{33}$ without directly calculating the values
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
68824
Show that $\frac{(3^{77}-1)}{2}$ is odd and composite
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
39943
Proving $\mathrm e <3$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
152630
showing that a group of order 45 is abelian
1702
Proving that there are infinitely many primes with remainder of 2 when divided by 3
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
125707
A simple proof (hopefully) for $2^x \neq 0$
83542
A natural problem in $\textrm{S}_2^\textrm{P}$?
53162
$13\mid4^{2n+1}+3^{n+2}$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
105405
Product of three consecutive positive integers is never a perfect power
77351
How to use Fermat's little theorem to find $50^{50}\pmod{13}$?