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Math Help - give an example

  1. #1
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    give an example

    Prove that if  a^n -1 is prime where a \in N  and n \geq 2,  then a =2  and n is prime
    How I can use the identity : a^{kl} -1 =  (a^k -1)(a^{k(l-1)} + a^{k(l-2)} + …+  a^{k }+1) to solve this Q ??
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  2. #2
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    Quote Originally Posted by flower3 View Post
    Prove that if  a^n -1 is prime where a \in N and n \geq 2, then a =2 and n is prime
    How I can use the identity : a^{kl} -1 =  (a^k -1)(a^{k(l-1)} + a^{k(l-2)} + +  a^{k }+1) to solve this Q ??

    Well, if n=kl is not a prime then, as you wrote, you have a^{kl} -1= (a^k -1)(a^{k(l-1)} + a^{k(l-2)} + +  a^{k }+1) , and this is a non-trivial factorization of a^n-1

    UNLESS a=2 ...

    Tonio
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