Question

Need help with a discrete math problem.

Answer 1

I have part (a) and (d) finished but need help with (b), (c) and (e).

Answer 2

So far for (b) I have the products of primes.

221 = 13 x 17 119 = 7 x 17 91 = 71 x 13

Answer 3

Also, the places with large spaces in part b and c and d are congruent signs.

Answer 4

4 (b) (i) states A1= 0 mod 13

we know A1= 13*17* a1 (where a1 is some integer)
if we divide A1 by 13 we get 17*a1 with 0 remainder
in other words, A1 = 0 mod 13

use that same reasoning for A1 mod 17

Answer 5

I don't get where the 17 came from in the second part

Answer 6

or would it be for the third part A1 = 17*13*a1?

Answer 7

question 4(b) (i) part 3: A1 = 0 mod 17

we know A1= 17*13*a1
divide by 17 and we get 0 remainder. so A1 = 0 mod 17

Answer 8

ah ok, awesome.

Answer 9

So I would need to use the same reasoning for ii and iii

Answer 10

yes

Answer 11

Alright, that makes sense, I'll do those later.

could you get me started on (c) real quick?

unfortunately gotta go to classes in a minute

Answer 12

4 (c) (i) A mod 7

that means do 3*(A1 mod 7) + 4*(A2 mod 7)+ ...
use 4 (b) to find the values of A1 mod 7 , A1 mod 7, etc

Answer 13

Awesome, thank you so much!

Answer 14

In case you don't notice, 1547=7*13*17

Answer 15

ah ok, makes sense.

Answer 16

Thanks again. :) I'll be back on in like 4 hours to finish.

Answer 17

Looking at 4 (a), I am not sure what it says.
At first I thought it left out an =
but now I think it left out a + sign ?

if so the problem is
\[ 221 a_1 + 7 b_1= 1 \]

we note that 221 =13*17, so it is co-prime with 7. In other words, the greatest common divisor is 1

if you use the extended Euclidean algorithm,
you should find a1= 2 and b1= -63
as a check: 221*2 -7*63= 1

now we can answer 4 (b) part 1: A1= 1 mod 7 this way:

use 4 (a) (i) to say
(221*2 + -63*7) mod 7 = 1 mod 7
(221*2) mod 7 + (-63*7) mod 7 = 1

we see -63*7 is evenly divisible by 7, so (-63*7) mod 7 = 0
we get

(221*2) mod 7 + 0 = 1
or
A1 mod 7 = 1

Answer 18

Ah, I see how that would make a difference.

It was actually supposed to be 221a1 - 7b1 = 1

so I ended up with 2 and 63 instead of -63.