Divisor Modulo Integer/Examples/8 modulo 12

Examples of Divisors Modulo $m$

In modulo $12$ division, $8$ has the following divisors:

$1, 2, 4, 5, 7, 8, 10, 11$

Proof

\(\ds 1 \times 8\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 2 \times 4\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 4 \times 5\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 2 \times 10\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 4 \times 8\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 4 \times 11\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 7 \times 8\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

\(\ds 8 \times 10\)

\(\equiv\)

\(\ds 8\)

\(\ds \pmod {12}\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factor modulo $n$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factor modulo $n$