Question

Need help with a discrete math problem.

Answer 1

Here is the problem

Answer 2

Here is what I have so far for part A.

Answer 3

@myininaya

Answer 4

Do you know if I did part A right?

Answer 5

So using what you did for part Ai
221=7(31)+4 equation 1
7=4(1) +3 equation 2
4=3(1) +1 equation 3

This implies => 4-3=1 by equation 3.
4-(7-4)=1 by equation 2.
4-7+4=1
2(4)-7=1
2(221-7(31))-7=1 by equation 1
2(221)-7(2*31)-7=1
2(221)-7(2*31+1)=1
2(221)-7(63)=1
That should be a true statement if I did arithmetic right.

Answer 6

I used your equations backwards to find a and b.

Answer 7

2(221)+7(-63)=1

Answer 8

Oh I see, so you basically just rewrite 1 as 2(221)-7(63)

Answer 9

yep
I'm assuming there is a plus sign there.

Answer 10

on your worksheet

Answer 11

some symbols are missing

Answer 12

where are the plus signs missing on the worksheet?

Answer 13

ai,aii,aii
and I think equal signs or some kinda symbols are missing on b and c and d.

Answer 14

well that would explain a lot :)

So the steps above basically show how to do part (i) right?

Answer 15

yea.

Answer 16

So you don't see signs on your end right?

Answer 17

Like you see what I see is missing?

Answer 18

no

Answer 19

Had that happen before on a homework already where the signs weren't there

Answer 20

makes it harder to understand lol

Answer 21

I think ai is either 221a+7b=1 or 221-7b=1
I think aii is 119a+13b=1 or 119a-13b=1
aiii is 91a+17b=1 or 91a-17b=1
I really think the teacher would put plus instead of minus. I could be wrong.

Answer 22

All of these you are suppose to find a and b.such that those statements are true

Answer 23

So you would do the part you did and work through it backwards to find a and b.

Answer 24

Like what I did with your equations.

Answer 25

ah ok, that helps a lot. I will see if I can work through (ii) and (iii) backwards then.

Answer 26

But you must put both ways on there.
The backwards and forwards part.

Answer 27

You know just to show work.

Answer 28

right right, So for (ii)

119 = 9(13) + 2 equation 1
13 = 6(2) + 1 equation 2
2 = 2(1) + 1 equation 3

This implies => 2-1=1 by equation 3

Answer 29

hmm, stuck here.

Answer 30

119 = 9(13) + 2 equation 1
13 = 2(6) + 1 equation 2
2 = 2(1) equation 3

---
By equation 2 we have 13-2(6)=1

Answer 31

we don't need equation 3

Answer 32

We are looking for where we have remainder 1

Answer 33

13=2(6)+1 gives us that

Answer 34

ah ok

Answer 35

Also it could be that you made the mistake that 2=2(1)+1

Answer 36

You wrote that part correctly on your paper.

Answer 37

oh I see, so something like 13-2(6) = 1?

Answer 38

Yes then we use equation 1.

Answer 39

119 = 9(13) + 2

=>
119-9(13)=2

so replace 2 in 13-2(6)=1

Answer 40

so 13-(119-(9(13))(6) = 1

Answer 41

Then put your 13's together and your 119's together.

Answer 42

how would I do that?

Answer 43

13-[119-9(13)](6) = 1
How would you put your like terms together in this:

x-[y-9(x)](6)
or
x-6[y-9x]

Answer 44

is there a way you can factor? I'm not exactly sure :/

Answer 45

Collect your like terms/simplify x-6[y-9x]
Distribute like so: x-6y+54x
Put like terms together.

Answer 46

55x-6y

Answer 47

If you noticed I just called 13 x and 119 y earlier because I thought it would be easier for you to see how to combine the 13's and 119's

Answer 48

55(13)-6(119)=1

Answer 49

Oh I see now :D

Answer 50

You do the last one!

Answer 51

ok

Answer 52

I will be back in like a few. I will check it when I come back.

Answer 53

ok sounds great

Answer 54

what do you have?

Answer 55

so,

91 = 5(17) + 6 equation 1
17 = 2(6) + 5 equation 2
6 = 1(5) + 1 equation 3

This implies => 6 - 5 = 1 by equation 3
6 - (17-2(6)) = 1 by equation 2
6 - 17 + 2(6) = 1
3(6) - 17 = 1
3(91 - 5(17) ) = 1 by equation 1

Answer 56

The last equation is 3[91-5(17)]-17=1?

Answer 57

oh yeah, accidentally dropped that

Answer 58

So we have 3(91)-15(17)-17=1

Answer 59

You give the final equation.

Answer 60

ok so,

3(91)-16(17) = 1

Answer 61

Yes so you should be able to identify what a and b are.

Answer 62

Well sorta since we really don't know what operation goes there, minus or plus. lol.

Answer 63

haha

Answer 64

hmm, I'm gonna check the homework real quick and see if he updated it.

Answer 65

no, still looks the same.

Answer 66

For the rest of this you might find this helpful that
a conguent to b (mod n) means there is some integer k such that nk=a-b

I'm going to have to come back tomorrow to openstudy because like I have to go. I have some things to prepare for tomorrow.
I'm sorry.

Answer 67

Ok cool, thanks so much for all the help though! :)

Answer 68

Np. Good luck on your math classes. You can do it. :)

Answer 69

Well I'll probably be working on it pretty late as it is due tomorrow :/

But I defiantly have a better understanding of the concepts now.

Answer 70

Well hopefully he gives you an extension. Some of it is hard to read because of the missing symbols.

Answer 71

We did part (a) and started part (b) right?

Like we didn't do the (i) (ii) and (iii) for part b right?

Answer 72

We didn't touch part b.

Answer 73

oh I thought what we were doing was the writing as the products of primes

Answer 74

we were just finding the integers, ah ok, makes sense now

Answer 75

lol. No all of what we did was for part A.

Answer 76

haha ok :D

Answer 77

Like ai was 221a+7b=1
we were looking for a and b such that statement was true.
The we did the same for aii and iii

Answer 78

right right

Answer 79

There was two parts: the forwards with euclidean algorithm and then working backwards through to find those integers.

Answer 80

Right, I'll make sure to write all that down on my solutions steps

I also have the solutions for part (d) and a little of part (b) in my notes, so hopefully that will help out.

Answer 81

I think everywhere else we can see that there is something missing we can assume it is suppose to be an equal sign I think.

Answer 82

After further thinking, maybe it could be a non-equal sign. lol since A1=221(2) does not equal 1 mod 7

Answer 83

Well, for some reason when I printed off the assignment so I could staple my work to the cover sheet all the signs magically appeared. Here is what it looked like, however, I already turned it in so it doesn't make much difference either way now. :P