mathschallenge.net logo

Power Divisibility

Problem

Consider the following results.

81minus1 = 7 = 7times1
82minus1 = 63 = 7times9
83minus1 = 511 = 7times73
84minus1 = 4095 = 7times585
85minus1 = 32767 = 7times4681

Prove that 8nminus1 is always divisible by 7.

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

Show Problem & Solution