Congruence (Number Theory)/Examples/5.74 congruent to -3.26 Modulo 3

Example of Congruence Modulo an Integer

$5 \cdotp 74 \equiv -3 \cdotp 26 \pmod 3$

Proof

\(\ds 5 \cdotp 74\)

\(=\)

\(\ds 3 \times 3 - 3 \cdotp 26\)

\(\ds \leadsto \ \ \)

\(\ds 5 \cdotp 74\)

\(\equiv\)

\(\ds -3 \cdotp 26\)

\(\ds \pmod 3\)

$\blacksquare$

Sources

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