Question

Find the multiplicative order of 5 and 7 in z16

Answer 1

$5\equiv5\mod{16}$
$5^2=25\equiv9\mod{16}$
$5^3\equiv5\cdot9\equiv45\equiv48-3\equiv-3\equiv13\mod{16}$
$5^4\equiv9^2\equiv81\equiv1\mod{16}$
$5^5\equiv5\cdot1\equiv5\mod{16}$

$7\equiv7\mod{16}$
$7^2\equiv49\equiv48+1\equiv1\mod{16}$
$7^3\equiv7\cdot1\equiv7\mod{16}$