# y = 3 x + 7 <mspace width="1em" /> ( mod <mspace width="0.333em" />

Banguizb 2022-07-03 Answered
$y=3x+7\phantom{\rule{1em}{0ex}}\left(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}4\right),\phantom{\rule{1em}{0ex}}x,y\in {\mathbb{Z}}_{4}$
$x=2,y=$??
Find the inverse function and verify the value of $y$.
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## Answers (1)

Isla Klein
Answered 2022-07-04 Author has 12 answers
Solve it like this (adding mod $4$ after everything of course)
$y=3x+7\phantom{\rule{0ex}{0ex}}y-7=3x\phantom{\rule{0ex}{0ex}}{3}^{-1}\left(y-7\right)={3}^{-1}3x\phantom{\rule{0ex}{0ex}}{3}^{-1}\left(y-7\right)=x$
So all you need to do is find the inverse of $3$ mod $4$.
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