1. ## need help about irreduciable?

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

Thanks.

2. (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.

3. 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 ?

4. Yes

5. Originally Posted by whipflip15
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.

6. Originally Posted by junbin
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.

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.

7. Originally Posted by whipflip15
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 ?

8. Originally Posted by junbin
144 mod 25 = 19. So an additive inverse mod 25 is 6. Isn't it ?
Yes

Originally Posted by junbin
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.

9. 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

10. Originally Posted by junbin
a multiplicative inverse of 25 is 4 because gcd(25,4)=1
Originally Posted by junbin
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 19×4 = 76 = 75 + 1 = 1 (mod 25).

11. 1. Given that x^2 + 3x + 4 irreducible over {0,1,2,3,4}
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

12. Originally Posted by whipflip15
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 ?

13. anyone has any idea ?