Divisible by 3?


A number is divisible by 3 if the sum of the digits is divisible by 3. How about a number of the type (22n – 1), where n is a positive integer? Can we show that it is always divisible by 3?
Hint
No need to use divisibility by 3 rule here, 
but a particular factoring rule: 
an – 1 = (a – 1)(an-1 + an-2 + … + a + 1).

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