Show that: `2^(4n)-2^n(7n+1)` is some multiple of the square of 14, where n is a positive integer.

(-i)^(4n+3), where n Is a positive integer.

Solve (x-1)^(n)=x^(n), where n is a positive integer.

Show that (-sqrt(-1))^(4n+3) =i , where n is a positive integer.

((1+i)/(1-i))^(4n+1) where n is a positive integer.

Show that ((-1+sqrt(3)i)/(2))^(n)+((-1-sqrt(3i))/(2))^(n) is equal to 2 when n is a multiple of 3 and 3 is equal to -1 when n is any other positive integer.

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

Show that one and only one out of n,n+2 or,n+4 is divisible by 3, where n is any positive integer.