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Math Help - for any prime p and any elements "a" of Zp, show irreducible

  1. #1
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    Red face for any prime p and any elements "a" of Zp, show irreducible

    The other question im stuck on is :

    For any prime p and any element a of Zp, show that x^(P) -a and x^(p) + a are irreducible over Zp
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    The other question im stuck on is :

    For any prime p and any element a of Zp, show that x^(P) -a and x^(p) + a are irreducible over Zp
    they are reducible not irreducible! each is a p power of a polynomial of degree one. can you solve the problem now?
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  3. #3
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    hint number 2: what is a^p in Zp?
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  4. #4
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    ok so a^p=a I found x^p -a to be reducible but still having trouble with x^p+a . I know x^p+a = (x+a)^p because Zp is a field with Char=p but not sure where to go from there.
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  5. #5
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    Quote Originally Posted by nikie1o2 View Post
    ok so a^p=a I found x^p -a to be reducible but still having trouble with x^p+a . I know x^p+a = (x+a)^p because Zp is a field with Char=p but not sure where to go from there.

    You can go from there and have a beer (if you're in USA and if you're over 21...) since you've just proved that x^p + a is a product of p linear

    factors and thus reducible, so you're done ( Corona is the best!)

    Tonio
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