## Power Divisibility

#### Problem

Consider the following results.

8

8

8

8

8

^{1}1 = 7 = 718

^{2}1 = 63 = 798

^{3}1 = 511 = 7738

^{4}1 = 4095 = 75858

^{5}1 = 32767 = 74681Prove that 8^{n}1 is always divisible by 7.

Problem ID: 204 (24 Jan 2005) Difficulty: 3 Star