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,...

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,...