$($a$)$ Let p be either $7,13,$ or $19.$ Show that if p doesn$$t divide a$,$ a$^1728=1$ mod p$.$

$($b$)$ Let p be either $7,13,$ or $19.$ Show that for any integer a$,$ a$^1729=$ a mod p$.$

$($c$)$ Show that for every a$,$ a$^1729=$ a mod $1729.$