Disprove if a<b then a^2 < b^2
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
85731
Prove by induction that $n! > n^2$
60348
How do I prove $F(a)=F(a^2)?$
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
108237
Show $a^p \equiv b^p \mod p^2$
131844
When does $(e^a)^b = e^{ab}$ hold?
86030
Prove or disprove - If a divides b and b divides a does a=b
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
15626
Relations of a~b iff b = ak^2
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$