Show that :
`( 3 + 3omega + 5omega^2 )^6 - ( 2 +6 omega + 2omega^2 )^3 = 0 `

(2 + 5 omega + 2 omega ^ (2)) ^ (6) = (2 + 2 omega + 5 omega ^ (2)) ^ (6) = 729

If omega,omega^(2) be imaginary cube root of unity then (3+3 omega+5 omega^(2))^(6)-(2+6 omega+2 omega^(2))^(3) is equal to

Let omega ne 1 be a complex cube root of unity. If ( 4 + 5 omega + 6 omega ^(2)) ^(n^(2) + 2) + ( 6 + 5omega^(2) + 4 omega ) ^(n ^(2) + 2) + ( 5+ 6 omega + 4 omega ^(2) ) ^( n ^(2) + 2 ) = 0 , and n in N , where n in [1, 100] , then number of values of n is _______.