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Is there a proof of dirichlets theorem that does not require complex analysis?

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I don't know, but I can't see how to dispose of Dirichlet (complex) characters...Besides this, complex analysis is very beautiful and useful stuff, and Dirichlet's Theorem's proof is very nice...with complex analysis. –  DonAntonio Dec 16 '12 at 2:47

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The proof given in A Classical Introduction to Modern Number Theory by Ireland and Rosen doesn't use anything you wouldn't learn outside of say a basic calculus course.

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Can I get a link to the proof somehow? –  Ethan Dec 16 '12 at 4:00
    
Its a copyrighted book, so I believe an online copy of the book is illegal. However, you can buy a copy here : amazon.com/Classical-Introduction-Modern-Graduate-Mathematics/…. You can probably borrow this book from a local university's library, I'd be very surprised if the library lacked a book as famous as this. –  dinoboy Dec 16 '12 at 7:56

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