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I don't really understand how to solve the equation $$47x \equiv 4 \mod 17.$$ If someone could help, that would be much appreciated. Thanks!

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As $47\equiv-4\pmod{17},$

$$47x\equiv4\pmod{17}\iff-4x\equiv4$$

As $(4,17)=1,$

$$-x\equiv1\iff x\equiv-1$$

$$\implies x\equiv-1+17$$

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  • $\begingroup$ Your last line is garbled... $\endgroup$ – TonyK Nov 26 '20 at 16:23
  • $\begingroup$ @TonyK, Now sure if I have understood you correctly . $\endgroup$ – lab bhattacharjee Nov 26 '20 at 16:25
  • $\begingroup$ Well you've fixed it now, haven't you? Initially it read $x\equiv -+17$. $\endgroup$ – TonyK Nov 26 '20 at 16:39

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