This exercise has also been posted yesterday at the cryptography help thread. Since my deadline for delivery has approached earlier I decided to move it here. I don't believe it is related to cryptography as much as Number's Theory.
Prove that the following is true:
11^n + 5^n = 0 (mod7) when n = 3 (mod6)
Hint: You can use (it is proven) that 11^3 = 1 (mod3) and 5^3 = -1 (mod3)
Thanks in advance for your time and help.