Question

Is there an ISBN that has the form : x - 315266-78-2?

Answer 1

This question I have right now in my math course, we've had null information about how to do it? could anyone explain to me how to?

Answer 2

@IrishBoy123 you know anything bout this?

Answer 3

ISBN is something to do with books and unique ID numbers

and that is everything i know, assuming it is actually correct :-)

Answer 4

I don't see how this is a question, ISBN's are on the back of your book, is it asking you to get a book with the certain ISBN maybe?

Answer 5

@Astrophysics no, you are suppose to show with math calculation if it is a true ISBN or not!

Answer 6

@perl

Answer 7

Oh, I have no idea then, sorry :\

Answer 8

It has to do with somekind of sequence, and congruity

Answer 9

we are studying residue class arithmetic or what it is called in english

Answer 10

Here is an example
ISBN numbers for published books.

The ISBN number for our textbook is 0-13-184-868-2.
The information is decoded in the first 9 digits. The last digit is for parity check
1 * a1 + 2 * a2 + ... + 9 * a9 = a10
Applying this to our textbook

1 * 0 + 2 * 1 + 3 * 3 + 4 * 1 + 5 * 8 + 6 * 4 + 7 * 8 + 8 * 6 + 9 * 8 = 255 = 2 mod 11



The sum of 9 digits is 255 and it equals to the last digit mod 11.

Answer 11

⇒ a10 = 4 eftersom 11 | 103 + 40 = 143
\[a _{1}, a _{2}, a _{3}, ..., a _{10}\] the numbers in ISBN
\[a _{10}\] is choosen like:
\[a _{1}+ 2a _{2}+ 3a _{3}+ ..., 9a _{9}+10a_{10}≡ 0 (mod 11)\]
if \[a_{10}=10\] you write X

Example ISBN=093603103a10
\[a_{10}\] is choosen like
\[1 · 0 + 2 · 9 + 3 · 3 + · · · + 9 · 3 + 10 · a_{10} = 103 + 10a_{10} ≡ 0 (mod 11)\]
⇒ \[a_{10} = 4 \] because \[11 | 103 + 40 = 143\]

Answer 12

ah wait I gotta write this down and see

Answer 13

so here I got
x+226=2 (mod10)?

Answer 14

so we need to check that
x - 315266-78-2 can be an isbn number, only if

1*x + 2*3 + 3*1 + 4*5 + 5*2 + 6 * 6 + 7*6 + 8*7 + 9*8 = 2 mod 11

Answer 15

x+226=2 mod 11

Answer 16

check again, I got x + 245 = 2 mod 11

Answer 17

1*x + 2*3 + 3*1 + 4*5 + 5*2 + 6 * 6 + 7*6 + 8*7 + 9*8 = x + 245

Answer 18

yea.. i got the same

Answer 19

so then should x+245/11 give something with the rest 2..

Answer 20

x + 245 = 2 mod 11
x = 2 - 245 mod 11
x = -243 mod 11
x = 10 mod 11

Answer 21

can you explain the last step?

Answer 22

but notice that 10 is not a choice for an isbn digit, since it has to be a digit from 0 to 9
so the answer is, there is no x

Answer 23

i mean from -243 to 10 mod 11

Answer 24

yeah but how did you make -243 mod 11 to 10 mod 11?

Answer 25

it is easier to use multiple of 11's

Answer 26

I am actually using my calculator for negative mod

Answer 27

x + 245 = 2 mod 11

with respect to 245 where is the closest multiple of 11 ?

Answer 28

22*11 = 242
23*11 = 253

Answer 29

245 = 3 mod 11 , so we can substitute
(x + 245) mod 11 = (x + 3) mod 11
now solve
(x+3) mod 11 = 2 mod 11
x = 2-3 mod 11
x = -1 mod 11

Answer 30

when you do negative integers, it is like going backwards with a clock

Answer 31

0 mod 11 = 11 mod 11
-1 mod 11 = 10 mod 11
-2 mod 11 = 9 mod 11
-3 mod 11 = 8 mod 11