Modulo Multiplication is Well-Defined/Examples

Examples of Use of Modulo Multiplication is Well-Defined

Modulo Multiplication: $19 \times 6 \equiv 11 \times 2 \pmod 4$

\(\ds 19\)

\(\equiv\)

\(\ds 11\)

\(\ds \pmod 4\)

\(\ds 6\)

\(\equiv\)

\(\ds 2\)

\(\ds \pmod 4\)

\(\ds \leadsto \ \ \)

\(\ds 19 \times 6 = 114\)

\(\equiv\)

\(\ds 11 \times 2 = 22\)

\(\ds \pmod 4\)

Modulo Multiplication: $2 \times 3 \equiv -6 \times 15 \pmod 4$

\(\ds 2\)

\(\equiv\)

\(\ds -6\)

\(\ds \pmod 4\)

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

\(\ds 3\)

\(\equiv\)

\(\ds 15\)

\(\ds \pmod 4\)

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

\(\ds \leadsto \ \ \)

\(\ds 2 \times 3 = 6\)

\(\equiv\)

\(\ds \paren {-6} \times 15 = -90\)

\(\ds \pmod 4\)