Congruence (Number Theory)/Examples/8 congruent to -1 Modulo 3

Example of Congruence Modulo an Integer

$8 \equiv -1 \pmod 3$

Proof

\(\ds 8\)

\(=\)

\(\ds 3 \times 3 - 1\)

\(\ds \leadsto \ \ \)

\(\ds 8\)

\(\equiv\)

\(\ds -1\)

\(\ds \pmod 3\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): congruence modulo $n$ (C.F. Gauss, 1801)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): congruence modulo $n$ (C.F. Gauss, 1801)