Solution of Linear Congruence/Examples

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 $t \in \Z$.