Modulo Addition is Well-Defined/Examples

Examples of Use of Modulo Addition is Well-Defined

Modulo Addition: $2 + 3 \equiv -6 + 15 \pmod 4$

We have:

\(\ds 2\)

\(\equiv\)

\(\ds -6\)

\(\ds \pmod 4\)

Congruence Modulo $4$: $2 \equiv -6 \pmod 4$

\(\ds 3\)

\(\equiv\)

\(\ds 15\)

\(\ds \pmod 4\)

Congruence Modulo $4$: $3 \equiv 15 \pmod 4$

\(\ds \leadsto \ \ \)

\(\ds 2 + 3 = 5\)

\(\equiv\)

\(\ds -6 + 15 = 9\)

\(\ds \pmod 4\)

Modulo Addition: $19 + 6 \equiv 11 + 2 \pmod 4$

We have:

\(\ds 19\)

\(\equiv\)

\(\ds 11\)

\(\ds \pmod 4\)

\(\ds 6\)

\(\equiv\)

\(\ds 2\)

\(\ds \pmod 4\)

\(\ds \leadsto \ \ \)

\(\ds 19 + 6 = 25\)

\(\equiv\)

\(\ds 11 + 2 = 13\)

\(\ds \pmod 4\)