$($b$)($i$)$ The number $7829$ is prime. Calculate $5$

$7831$ mod $7829$

$[6$ marks$]$

$($ii$)$ Calculate $373,755,007,178$ x $389,291,774,965$ mod $10.$

$[6$ marks$]$

$($iii$)$ Calculate $9$

$-1$ mod $11.$

$[6$ marks$]$

$($iv$)$ Calculate $1364$ mod $11$