Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Does there exist an odd prime $p>3$, and integers $m>2$ and $n_k>0$ such that

$$ p^{\sum_{k=1}^m n_k} \equiv 1 \bmod \prod_{k=1}^m (p^{n_k}-1) ? $$

where if some n_i are the same , the same number appears at most r(n,p) times. r(n,p) is the number of irreducible polynomials of degree n over the finite field F_p.

share|improve this question
    
m is larger than 1 –  mason Apr 15 '12 at 15:53
4  
Yes, for example $p=3$. See here: mathoverflow.net/questions/81816/… –  Ralph Apr 15 '12 at 16:22
    
It may be helpful, if you could provide more background about your question. In particular, why do you need p>3 and what's the reason for the condition involving r(n,p) ? –  Ralph Apr 16 '12 at 0:02
    
the decomposition of a polynomial –  mason Apr 16 '12 at 14:53
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.