Question

Determine whether the congruence is true or false. 7equiv 21 mod 3

Congruence
ANSWERED
asked 2021-01-19
Determine whether the congruence is true or false.
\(7\equiv 21\ mod\ 3\)

Answers (1)

2021-01-20
Calculation:
The congruence is \(7 \equiv 21\ mod\ 3\).
Consider \(\frac{7-21}{3}\),
\(\frac{7-21}{3}\equiv 14/3\)
Because \(-14/3\) is not an integer, \(7 \equiv 21\ mod\ 3\) is a false congruence.
Hence, the congruence \(7 \equiv 21 mod\ 3\) is false.
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