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Power Divisibility

Problem

Consider the following results.

8¹

1 = 7 = 7

1
8²

1 = 63 = 7

9
8³

1 = 511 = 7

73
8⁴

1 = 4095 = 7

585
8⁵

1 = 32767 = 7

4681

Prove that 8ⁿ1 is always divisible by 7.

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

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