) find an integer x, 0 ≤ x ≤ 40, that satisfies 34x = 5 (mod 41). show your work

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15-01-2018
Mathematics

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) find an integer x, 0 ≤ x ≤ 40, that satisfies 34x = 5 (mod 41). show your work

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Rod44 Rod44 · Answer 1 · 2018-01-15T17:23:44+01:00

Rod44 Rod44

15-01-2018

34x=41n+5, x=((34+7)n+5)/34=n+7n/34+5/34=n+(7n+5)/34
We require 7n+5 to be a multiple of 34.
7n+5=34, 7n+5=68, 7n=63 so n=9.
34x=41×9+5=369+5=374, x=11.
An integer below 40 satisfying 34x=5(mod 41) is x=11.
34×11=374=5(mod 41) because 374/41=9 rem 5.

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