Question

Find all whole number solutions of the congruence equation. (2x + 1)equiv 5 mod 4

Congruence
ANSWERED
asked 2020-11-24
Find all whole number solutions of the congruence equation.
\((2x + 1)\equiv 5\ mod\ 4\)

Answers (1)

2020-11-25
Step 1
Consider the given congruence equation.
\((2x + 1)\equiv 5\ mod\ 4\)
Step 2
Substitute each whole number less than 4 into the congruence equation.
\(x=0.2(0)+1\equiv 5\ mod\ 4\) a solution
\(x=1.2(1)+1\neq 5\ mod\ 4\) not a solution
\(x=2.2(2)+1\equiv 5\ mod\ 4\) a solution
\(x=3.2(3)+1\neq 5\ mod\ 4\) a solution
The solution between 0 and 3 is 0 and 2.
The remaining solutions are determined by repeatedly adding the modulus,4,to these solutions.
Hence, the solutions to the congruence equation 0,2,4,6,8,10,...
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