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

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

Physics
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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?
@IrishBoy123 you know anything bout this?
ISBN is something to do with books and unique ID numbers and that is everything i know, assuming it is actually correct :-)

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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?
@Astrophysics no, you are suppose to show with math calculation if it is a true ISBN or not!
Oh, I have no idea then, sorry :\
It has to do with somekind of sequence, and congruity
we are studying residue class arithmetic or what it is called in english
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.
⇒ 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 \[11 | 103 + 40 = 143\]
ah wait I gotta write this down and see
so here I got x+226=2 (mod10)?
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
x+226=2 mod 11
check again, I got x + 245 = 2 mod 11
1*x + 2*3 + 3*1 + 4*5 + 5*2 + 6 * 6 + 7*6 + 8*7 + 9*8 = x + 245
yea.. i got the same
so then should x+245/11 give something with the rest 2..
x + 245 = 2 mod 11 x = 2 - 245 mod 11 x = -243 mod 11 x = 10 mod 11
can you explain the last step?
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
i mean from -243 to 10 mod 11
yeah but how did you make -243 mod 11 to 10 mod 11?
it is easier to use multiple of 11's
I am actually using my calculator for negative mod
x + 245 = 2 mod 11 with respect to 245 where is the closest multiple of 11 ?
22*11 = 242 23*11 = 253
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
when you do negative integers, it is like going backwards with a clock
0 mod 11 = 11 mod 11 -1 mod 11 = 10 mod 11 -2 mod 11 = 9 mod 11 -3 mod 11 = 8 mod 11
|dw:1442861614220:dw|
imagine we have an 11 hour clock
|dw:1442861679974:dw|
-1 aclock = 10 aclock mod 11 -2 aclock = 9 aclock mod 11 , etc
also because -1 mod 11 = (-1 + 11 ) mod 11 = 10 mod 11
thats the easiest way to see it. or you can use definition of mod a = b mod n iff b -a is divisible by n -1 = 10 mod because 10 -(-1) is divisible by 11
I got it perl:D thanks alot, but the answear is it isnt a ISBN just because it have to be a integer between 1 and 9?
between 0 and 9 i mean
the answer is, there is no such ISBN, since the only way it would work is if x = 10 but the possible choices for x is 0 - 9 .
the only way the total x + 245 can equal 2 mod 11 is if x is 10. but that is not possible for the isbn, x must be integer 0 through 9
@perl thanks alot! :D

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