228

a)
$3972=1324\cdot3+0$
$3576=1192\cdot3+0$
$564=188\cdot3+0$
$3972-3576\cdot576\equiv0-0\cdot0=0\left(mod\ 6\right)$
jakojäännös 0
b)

$87=17\cdot5+2$

$87\equiv2\left(mod\ 5\right)$

$109=21\cdot5+4$
$109\equiv4\ \left(mod\ 5\right)$
$3=1\cdot5-2$
$4=1\cdot5-1$
$87\cdot109+3\cdot4^{23}\equiv2\cdot4-2\cdot\left(-1\right)^{23}=8+2=10=2\cdot5+0\ \left(mod\ 5\right)$
jakojäännös 0