How can I prove that 2222−1 is divisible by three?
I already have decomposed the following one: (2111−1)(2111+1) and I understand I should just prove that (2111−1) is divisible by three or that (2111+1) is divisible by three. But how can I solve this problem?
Answer
The routine way is to invoke Fermat's little theorem: ap−1−1≡0(modp) for gcd(a,p)=1.
Plug in a=2111,p=3.
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