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September 7th, 2019, 01:34 PM   #1
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Math Focus: Elementary Math
Equation with natural variable

$\displaystyle \lfloor n/1 \rfloor + \lfloor n/2 \rfloor +...+\lfloor n/(n-1) \rfloor =7\; $, n-natural .

To write it better : $\displaystyle \sum_{j=1}^{n-1} \displaystyle \lfloor \frac{n}{j} \displaystyle \rfloor =7 \; $ ; n=? , Method Required !

Last edited by idontknow; September 7th, 2019 at 01:38 PM.
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September 8th, 2019, 03:27 AM   #2
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$\displaystyle m_1 =\lfloor 7/2 \lfloor $ and $\displaystyle m_{2} =1+m_1 $.

$\displaystyle M=\frac{1+2m_1 }{2}=3,5$. Number of elements is $\displaystyle \lfloor 3,5 \rfloor =3 $ which is n+1 .So $\displaystyle n=4$.

To verify : [4]+[4/2]+[4/3] =4+2+1=7 .
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