Testwiki:Reference desk/Archives/Mathematics/2011 December 22

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December 22

Linear Programming and Graph theory

Can someone suggest a good resource (book, or online notes) which I can read to learn about applying linear programming to optimization problems in graph theory? I am currently reading from Schrijver's Combinatorial Optimization but that book is very big (around 2000 pages) and has a lot of other stuff. I am not sure I will be able to wade through all of that. Does someone have any other recommendation? Thanks -Shahab (talk) 04:57, 22 December 2011 (UTC)

Primitive Roots

Given a prime p, which is known to be one more than a power of two, is there an analytic way of finding a primitive root mod p? Thanks. 92.19.236.79 (talk) 21:59, 22 December 2011 (UTC)

The only known primes of the form $2^n+1$ for n > 0 are the Fermat primes 3, 5, 17, 257, 65537. Of these, trial and error shows that 2 is a primitive root of 3 and 5, and 3 is a primitive root of 17, 257 and 65537. There is no known simple formula for finding primitive roots in the general case. Gandalf61 (talk) 13:33, 23 December 2011 (UTC)

Thanks. 92.19.231.140 (talk) 14:12, 23 December 2011 (UTC)

You might also want to think about the multiplicative group; the order and structure of that group; the possible orders of the elements of the group; and what the order of a quadratic non-residue might be. Ansatz (talk) 22:24, 23 December 2011 (UTC)