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Math Help - need help about irreduciable?

  1. #1
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    Exclamation need help about irreduciable?

    Is  x^2 + 3x + 4 is irreducible over {0,1,2,3,4}?

    Thanks.
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  2. #2
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    (Assuming you mean \mathbb{Z}_5.)
    If it is reducible it must have a linear factor so just evaluate the polynomial for each value and if all are nonzero than it is irreducible.
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  3. #3
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    thank you.
    so it will be something like:

    x=0: 0^2 + 3x0 + 4 = 4
    x=1: 1^2 + 3x1 + 4 = 3
    x=2: 2^2 + 3x2 + 4 = 4
    x=3: 3^2 + 3x3 + 4 = 2
    x=4: 4^2 + 3x4 + 4 = 2

    so it's irreducible.

    is it correct ?
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  4. #4
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    Yes
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  5. #5
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    Quote Originally Posted by whipflip15 View Post
    Yes
    thank you very much.

    i have others problems:

    Does 144 mod 25 have an additive inverse mod 25. If yes, give it.
    Does 144 mod 25 have an multiplicative inverse mod 25. If yes, give it.

    I dont really understand about additive inverse and multiplicative inverse. could you help me please ?
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  6. #6
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    Quote Originally Posted by junbin View Post
    thank you very much.

    i have others problems:

    Does 144 mod 25 have an additive inverse mod 25. If yes, give it.
    Does 144 mod 25 have an multiplicative inverse mod 25. If yes, give it.

    I dont really understand about additive inverse and multiplicative inverse. could you help me please ?
    An additive inverse of 144 mod 25 is a number which you add to it to get 0 mod 25.
    An multiplicative inverse of 144 mod 25 is a number which you multiply to it to get 1 mod 25. x has a multiplicative inverse modulo n iff gcd(x,n)=1.

    Can you answer it now? You may want to note that 144 = 19 mod 25.
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  7. #7
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    Quote Originally Posted by whipflip15 View Post
    An additive inverse of 144 mod 25 is a number which you add to it to get 0 mod 25.
    An multiplicative inverse of 144 mod 25 is a number which you multiply to it to get 1 mod 25. x has a multiplicative inverse modulo n iff gcd(x,n)=1.

    Can you answer it now? You may want to note that 144 = 19 mod 25.
    144 mod 25 = 19. So an additive inverse mod 25 is 6. Isn't it ?

    and a multiplicative inverse of 25 is 4 because gcd(25,4)=1

    Is that correct ?

    if i do it on the test, I just write something like that or I need to explain something else more ?
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  8. #8
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    Quote Originally Posted by junbin View Post
    144 mod 25 = 19. So an additive inverse mod 25 is 6. Isn't it ?
    Yes

    Quote Originally Posted by junbin View Post
    and a multiplicative inverse of 25 is 4 because gcd(25,4)=1

    Is that correct ?
    25 does not have an inverse because 25 is congruent to 0. You want to find the inverse of 19. We know an inverse exists because gcd(19,25)=1.
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  9. #9
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    25 does not have an inverse because 25 is congruent to 0. You want to find the inverse of 19. We know an inverse exists because gcd(19,25)=1.
    i still dont really understand about that. could you please explain more?

    thanks
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  10. #10
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    Quote Originally Posted by junbin View Post
    a multiplicative inverse of 25 is 4 because gcd(25,4)=1
    Quote Originally Posted by junbin View Post
    i still dont really understand about that. could you please explain more?
    You got the right answer, namely 4, but you embedded it in an "explanation" that is complete nonsense.

    What you should have said is that the multiplicative inverse of 144 (mod 25) is 4, because 144 = 19 (mod 25) and 194 = 76 = 75 + 1 = 1 (mod 25).
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  11. #11
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    1. Given that x^2 + 3x + 4 irreducible over {0,1,2,3,4}
    a. add (3x+2) and (4x+1)
    b. multiply (3x+2) and (4x+1)
    c. find the additive inverse of (3x+2)
    d. find the multiplicative inverse of (4x+1)

    preparing for the final ... someone help me pls

    thanks
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  12. #12
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    Quote Originally Posted by whipflip15 View Post
    An additive inverse of 144 mod 25 is a number which you add to it to get 0 mod 25.
    An multiplicative inverse of 144 mod 25 is a number which you multiply to it to get 1 mod 25. x has a multiplicative inverse modulo n iff gcd(x,n)=1.

    Can you answer it now? You may want to note that 144 = 19 mod 25.
    so does 0 have a additive inverse or multiplicative inverse mod 18 ?

    the additive inverse is 0 or there is no additive inverse ?

    there is no multiplicative inverse, isn't it ?
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  13. #13
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    anyone has any idea ?
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