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Find the integer $n$, $0 \le n \le 5$, such that \[n \equiv -3736 \pmod{6}.\]

 Mar 29, 2019
 #1
avatar+110093 
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Find the integer \(n, \;\;where \;\;\;0 \le n \le 5, \,\;\;such\; that \;\;n \;\equiv -3736 \pmod{6}. \)

 

-3736/6 = -622.6666666666666667 = -622+ - 4/6

 

n=-4mod6 = (-4+6) mod 6 =    2 mod 6

n=2

 

 

Edited: I made a super stupid careless error.  

 Mar 29, 2019
edited by Melody  Mar 29, 2019
 #2
avatar+25471 
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Find the integer \(n\), \(0 \le n \le 5\), such that \(n \equiv -3736 \pmod{6}\).

 

\(\begin{array}{|rcll|} \hline \mathbf{n} &\mathbf{\equiv}& \mathbf{-3736 \pmod{6} } \\\\ n +3736 &=& 6m \quad | \quad m\in \mathbb{Z} \\ n &=& 6m -3736 \quad | \quad m=\left\lfloor\dfrac{3736}{6} + 1 \right\rfloor \\ n &=& 6\left\lfloor\dfrac{3736}{6} + 1 \right\rfloor -3736 \\ n &=& 6\cdot 623 -3736 \\ n &=& 3738 -3736 \\ \mathbf{n} &\mathbf{=}& \mathbf{2} \\ \hline \end{array}\)

 

laugh

 Mar 29, 2019

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