let $a,b,c \in \mathbb{N}$, $\left \lfloor x \right \rfloor$ denote the greatest integer $\leq x$ and $min\left \{x,y \right \}$ denote the minimum of $x$ and $y$
prove or disprove that,
\[c \cdot \left \lfloor \frac{a}{b} \right \rfloor\ - \left \lfloor \frac{c}{a} \right \rfloor\ \cdot \left \lfloor \frac{c}{b} \right \rfloor\ \leq c \cdot min\left \{ a,b \right \}\]
A general rule or not
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
-
- Posts:461
- Joined:Wed Dec 15, 2010 10:05 am
- Location:Dhaka
- Contact:
Re: A general rule or not
$c=1,a=2^n,b=2$
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )