Hello, terencet!

I have a proof ... hope it's acceptable.

For , use congruence theory to establish: .

We have: .

. . . . . .

. . . . . .

. . . . . .

We raise 1 to an integral power and take the cube root.

. . Its value is 1.

We raise -1 to anoddpower and take the cube root.

. . Its value is -1.

The expression becomes: .

Therefore: is divisible by 13.