If n >= 1 is an integer, prove that 2^(2n) - 1 is divisible by 3. Is there a formal way to prove this or can I just demonstrate it by plugging in n = 1,2,3,etc?

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Proving by "plugging in" would involve an infinite number of cases.

try using induction

My problem is the only induction I know is plugging examples in!

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