Sunday, 25 May 2014

number theory - How do I prove divisibility by 3 without induction?

How do I prove that:




  1. $3$ divides $4^n-1$, where $n$ is a natural number, and



  2. $3$ divides $n^3-n$, where $n$ is a natural number?




All without induction?(only number theory)



Thanks !

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