17x-3-mod-29-

Question Number 110519 by bobhans last updated on 29/Aug/20

17 x \equiv 3 (\mod 29)

Commented by kaivan.ahmadi last updated on 29/Aug/20

17 x \overset{29}{\equiv} 3 \Rightarrow 34 x \overset{29}{\equiv} 6 \Rightarrow 5 x \overset{29}{\equiv} 6 \Rightarrow 30 x \overset{29}{\equiv} 36 \Rightarrow

x \overset{29}{\equiv} 7 \Rightarrow x = 29 k + 7; k \in Z

Commented by Rasheed.Sindhi last updated on 29/Aug/20

⊓ \overset{∙}{∣} ⊏ \exists \underset{∙}{∣}

Answered by bemath last updated on 29/Aug/20

we want to work out a multiplicative

inverse of 17 (\mod 29)

\to 17 \times 12 = 1 (\mod 29)

so we have 12 \times 17 x \equiv 12 \times 3 (\mod 29)

\Rightarrow x \equiv 36 (m o d 29)

\Rightarrow x \equiv 7 (\mod 29) or we got

\Rightarrow x = 7 + 29 k .

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