Question

(Ancient chinese problem) A band of 17 pirates stole a sack of gold coins , when they tried to devide the fortune into equal portions , 3 coins remained .In the ensuring brawl over this time an equal division left 10 coins . Again an argument developed in which another pirate was killed . but now the total fortune was evenly distributed among the survivor . what was the last number of coins that could have been stolen ?

Answer 1

ughhh its the same qs :|
ok type the equations

Answer 2

x = 3 mod 17
x = 10 mod 16
x = 0 mod 15 ?

Answer 3

ok lets do it without using chinese

Answer 4

ok thats right.. now since gcd(17,16,15)=1 use chinese

Answer 5

why?

Answer 6

without chinese ok cool :)

Answer 7

no, i mean, what is the chinese remainder. please teach

Answer 8

we did chinese in last problem already,
so lets do it without chinese so that we dont need to prove chinese remainder theorem here

Answer 9

take last congruence,
x = 0 mod 15

=>

x = 15k

Answer 10

well i saw the solution already, but whats the logic behind chinese

Answer 11

you want to know the logic behind chinese ?
or the solution to this problem, w/o using chinese ? :)

cuz u were asking for a solution w/o chinese in earlier post...

Answer 12

i dont understnad this pellet

Answer 13

i am frustrated as heck

Answer 14

you deserve to :o

Answer 15

perl ok lets solve it using chinese (to intruduce u chinese thm ) then prove it so u cud see the logic of it k ??

Answer 16

ok

Answer 17

ok so u got the three equations
x = 3 mod 17
x = 10 mod 16
x = 0 mod 15
sice gcd(17,16,15)= 1 u can apply chinese thm

Answer 18

now u got
c1=3
c2=10
c3=0

Answer 19

ok

Answer 20

whats teh chinese remainder theorem?

Answer 21

nw u need to convert it to
m x =1 mod n formulla ok ?

Answer 22

why?

Answer 23

sorry i ask a lot of questions

Answer 24

cuz
if gcd(a,n)=1 ,then the linear congruence ax=b(mod n) has a unique sol modulo n

then congruence ax=1 mod n has a unique solution this is called (multiplicasive) inverse of a modulo n

Answer 25

why does it need to be a unique solution

Answer 26

you keep saying unique solution, is this significant

Answer 27

lol know wat thats not me who saying its the thm check it in google :P

Answer 28

why do we need to change to mx = 1 mod n?

Answer 29

do you have a number theory book i can read

Answer 30

youre terrible at explaining this ,

Answer 31

whats next >