## amistre64 3 years ago so what we learned today .... if a doesnt divide b, but a divides bc; then a divides c.

1. amistre64

we also learned that if a divides bc, then a divides bcn ..... 30 minutes of my life gone :/

2. KingGeorge

Believe it or not, that's not inherently obvious. Depending on what structures you're using, if a doesn't divide b, but a does divide bc, it doesn't necessarily divide c.

3. amistre64

number theory ... :)

4. inkyvoyd

I'ma delete this shortly afterward, but can anyone help me http://openstudy.com/study#/updates/5064b1f2e4b0583d5cd3facc Also, does that apply for matrix algebra?

5. amistre64

mattrix algebra has quirks in that its .. cant recall. ring, field, group ??

6. KingGeorge

Number theory is an easy example, but you can define a ring with zero divisors, and suddenly, if ab=0, then neither a nor b must be 0.

7. inkyvoyd

o.o show me the logic!

8. amistre64

teacher did show us at the begining of the year about her thesis work on abstract algebra and made us write up Zmod 12 tables for addition and multiplication

9. KingGeorge

Zmod12 is a nice example. 2*6=0=3*4

10. inkyvoyd

No that's not helpful I don't understand zmods lool

11. KingGeorge

2*6 mod 12=0 If you understand modular multiplication, it's what you would imagine Zmod12 would be.

12. amistre64

if a not| b; the (a,b)=1; therefore 1 = ax+by multiply each side by c c = acx+bcy a|acx a|bcy , it was given in the thrm that a|bc therefore a | (acx+bcy) a | c

13. amistre64

all the 0 mod 12s have no recipricals :)

14. amistre64

.... er, no multiplicative inversai

15. inkyvoyd

I look at wikipedia and see funny symbols. http://en.wikipedia.org/wiki/Modular_arithmetic I quit this party.

16. amistre64

There must be some way out of here, said the joker to the thief. There's too much confusion ... I can't get no relief

17. KingGeorge

Well, if it's coprime to 12 it has a multiplicative inverse....

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