Solution of Linear Congruence/Examples
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Examples of Solutions of Linear Congruences
Solution to $5 x = 4 \pmod 3$
Let $5 x = 4 \pmod 3$.
Then:
- $x = 2 + 3 u$
where $u \in \Z$.
Solution to $7 x = 6 \pmod 5$
Let $7 x = 6 \pmod 5$.
Then:
- $x = 3 + 5 u$
where $u \in \Z$.
Solution to $9 x = 8 \pmod 7$
Let $9 x = 8 \pmod 7$.
Then:
- $x = 4 + 7 t$
where $t \in \Z$.
Solution to $6 x = 5 \pmod 4$
Let $6 x = 5 \pmod 4$.
Then $x$ has no solution in $\Z$.
Solution to $10 x = 8 \pmod 6$
Let $10 x = 8 \pmod 6$.
Then:
- $x = 4 + 7 t$
where $t \in \Z$.
Solution to $12 x = 9 \pmod 6$
Let $12 x = 9 \pmod 6$.
Then $x$ has no solution in $\Z$.
Solution to $325 n = 11 \pmod 3$
Let $325 n = 11 \pmod 3$.
Then:
- $x = 2 + 3 t$
where $t \in \Z$.