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# If $n \equiv 43 \pmod{60}$, then what is the residue of $n$ modulo 6?

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If $n \equiv 43 \pmod{60}$, then what is the residue of $n$ modulo 6?

Mellie  Jul 13, 2015

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$$\small{\text{ If n \equiv 43 \pmod{60}, then what is the residue of n modulo 6? }}$$

$$\small{\text{ \begin{array}{lrcl} (1) & n - 43 &=& 60\\ (2) & n-x &=& m\cdot 6 \\ \\ \hline \\ (1)-(2) & n-43 - n + x &=& 60 - m\cdot 6 \\ & -43 + x &=& 60 - m\cdot 6 \\ &x &=& 60+43- m\cdot 6 \\ &x &=& 103- m\cdot 6 \qquad | \qquad m =17 \mathrm{~~lowest ~positive ~integer}\\ &x &=& 103-102\\ & \mathbf{x} & \mathbf{=} & \mathbf{1 } \end{array} }}\\$$

the residue of n modulo 6 is 1

heureka  Jul 14, 2015
#1
+19651
+15

$$\small{\text{ If n \equiv 43 \pmod{60}, then what is the residue of n modulo 6? }}$$

$$\small{\text{ \begin{array}{lrcl} (1) & n - 43 &=& 60\\ (2) & n-x &=& m\cdot 6 \\ \\ \hline \\ (1)-(2) & n-43 - n + x &=& 60 - m\cdot 6 \\ & -43 + x &=& 60 - m\cdot 6 \\ &x &=& 60+43- m\cdot 6 \\ &x &=& 103- m\cdot 6 \qquad | \qquad m =17 \mathrm{~~lowest ~positive ~integer}\\ &x &=& 103-102\\ & \mathbf{x} & \mathbf{=} & \mathbf{1 } \end{array} }}\\$$

the residue of n modulo 6 is 1

heureka  Jul 14, 2015