Key to "Solve the following linear congruence: 17x congruence 3(mod"

ringearV

Answered question

2021-02-25

Solve the following linear congruence:

17 x c o n g r u e n c e 3 (m o d 210)

Answer & Explanation

Isma Jimenez

Skilled2021-02-26Added 84 answers

Step 1 Given:
$17 x \equiv 3 (m o d 210)$
Therefore,
$x \equiv 17^{- 1} * 3 (m o d 210)$
Find: $17^{- 1} (m o d 210)$
$210 = 17 \times 12 + 6$
$17 = 6 \times 2 + 5$
$6 = 5 \times 1 + 1$
Trace the steps backward.
$1 = 6 - 5$
$= 6 - (17 - 6 * 2)$
$= 3 * 6 - 17$
$= 3 (210 - 17 * 12) - 17$
$3 * 210 - 36 * 17 - 17$
$3 * 210 - 37 * 17$
Thus, $17^{- 1} (m o d 210) = - 37 (m o d 210) = 173 (m o d 210)$
Step 2 Hence,
$x \equiv 17^{- 1} * 3 (m o d 210)$
$\equiv 173 * 3 (m o d 210)$
$\equiv 519 (m o d 210)$
$\equiv 99 (m o d 210)$
Thus, $x \equiv 99 (m o d 210)$
Therefore, $17 \times 99 = 1683 \equiv 3 (m o d 210)$
Step 3 Result:
Thus, $x \equiv 99 (m o d 210)$
Therefore, $17 \times 99 = 1683 \equiv 3 (m o d 210)$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Didn't find what you were looking for?