Prove that for any two numbers $0 \leq a < b \leq m - 1$ it is not possible that $m|b - a$
30725
Why are naturals < modulus equal if congruent? [uniqueness of remainder]
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
13012
Why can a = b imply 2 = 1?
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
93771
Prove that for any set $A$ there is some $x \notin A$
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
32754
Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?