how could i prove that a cubic number $ u^3 $ is always of the form $ 9k+n $ where $n=0,1,2,3,4,\ldots,8$
can a similar proof be made to prove that a power of n $ n^k $ is of the form
$ am+b$ where k,m,a,b,u and n are integers $a=a(m) $ and $ b=0,1,2,3,\ldots,a-1 $
what congruence should i solve ? apparently i should study the congruence
$ u^3=b \pmod 9$ but i have no idea how to solve this.