One problem about number theory

  • #1

Homework Statement



Let [tex]p\ge 2[/tex]. Prove if [tex]2^p-1[/tex] is prime, then [tex]p[/tex] must be prime.

Homework Equations





The Attempt at a Solution



I am a physics student. I need help from those studying mathematics. Thank you very much!
 

Answers and Replies

  • #2
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Assume that p is NOT prime, then we can write p=ab, with a and b nontrivial.

Try to find a factorization of [tex]2^{ab}-1=(2^a)^b-1[/tex]...

(HINT: what does [tex]x^n-y^n[/tex] equal?)
 

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