Step by step solution to "Find a complete set of mutually incogruent solutions...."

permaneceerc

Answered question

2021-03-23

Find a complete set of mutually incogruent solutions.

7 x \equiv 5 \pm o d {11}

Gennenzip

Skilled2021-03-25Added 96 answers

Step 1
Multiply both sides by 3 in the given congruence equation

7 x \equiv 5 \pm o d {11}

and simplify using concept of congruence.

7 x \equiv 5 \pm o d {11}

3 \cdot 7 x \equiv 3 \cdot 5 \pm o d {11}

21 x \equiv 15 \pm o d {11}

- x \equiv 4 \pm o d {11}

Step 2
Now multiply by -1 in the equation

- x \equiv 4 \pm o d {11}

and use the congruence

- 4 \pm o d {11} \equiv 7

to find the value of x.

- x \equiv 4 \pm o d {11}

- 1 (- x) \equiv - 4 \pm o d {11}

x \equiv 7 \pm o d {11}

Since

x \equiv 7 \pm o d {11}

means

\frac{11}{x} - 7

therefore x-7 = 11k where k is an integer.
Hence x=7+11k. The set form of the solution is

\leq f t {7 + 11 k . k \in Z r i g h t}

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