Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Congruence equation  ?

Find all the whole number solutions of the congruence equation

 (3x + 4) = 5mod 11 

3 Answers

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  • Ian H
    Lv 7
    2 months ago

    3x + 4 congruent to 5(mod 11)

    3x congruent to 1(mod 11) = 11n + 1 ==> 12, 23, 34, 35, 56, 67,78, etc

    Selecting whole number solutions only,

    x = 4, 15, 26, etc, which is 11n + 4 or 4(mod 11)

  • ?
    Lv 7
    2 months ago

    solve 3 x + 4 congruent 5 (mod 11)

    Solution in the least residue system:

    x congruent 4 (mod 11)

    General solution:

    x = 11 n + 4 and n element Z

  • 2 months ago

    Note that "5 mod 11" has positive members 5, 16, 27, 38, 49, 60, 71, 82, etc.

    For x to be a whole number, we must select only the members congruent to 4 mod 3, which are

    16, 49, 82, 115, 148, etc.

    Then x = 4, 15, 26, 37, 48, etc.

    More generally, x = 4 mod 11.

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