My Math Forum Equation with natural variable

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 September 7th, 2019, 12:34 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 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 12:38 PM.
 September 8th, 2019, 02:27 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 $\displaystyle m_1 =\lfloor 7/2 \lfloor$ 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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