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

Thanks.

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- Dec 7th 2008, 11:30 PM #1

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- Dec 8th 2008, 01:37 AM #2

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- Dec 8th 2008, 01:07 PM #3

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- Dec 8th 2008, 01:14 PM #4

- Dec 8th 2008, 01:17 PM #5

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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 ?

- Dec 8th 2008, 01:31 PM #6

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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.

- Dec 8th 2008, 01:47 PM #7

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- Dec 8th 2008, 02:35 PM #8

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- Dec 8th 2008, 10:34 PM #9

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- Dec 9th 2008, 02:08 AM #10
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 19×4 = 76 = 75 + 1 = 1 (mod 25).

- Dec 11th 2008, 05:03 PM #11

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- Dec 11th 2008, 07:00 PM #12

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- Dec 12th 2008, 07:36 AM #13