Congruence (Number Theory)/Examples/5.74 congruent to -3.26 Modulo 3
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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 $n$ (C.F. Gauss, 1801)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): congruence modulo $n$ (C.F. Gauss, 1801)