Question

a=713 b=437
Find the gcd(a,b). Find two integers x,y such that 22=xa+yb

Answer 1

now the gcd is 23 that is easy to fin but how can I find x,y?

Answer 2

22=713x+437y
22=23(31x+19y)
22/23 =31x+19y
22=713x+437y

- so after this i think that you need checking two cases

1. when x=0 than y= 22/437
2. when y=0 than x= 22/713

- so this is just one my opinion from this all (i am not sure that is right sure -- sorry )

Answer 3

Has to be integers

Answer 4

sorry you think that after thses calcules will be possibill getting integers too ?

Answer 5

Now I have 8*713-13*437=23
I know how to do that. Now I would need to solve 1=ax+by

Answer 6

I believe it has no solutions but Im not sure

Answer 7

- so i understand your opinion but the result dont need to be 22 ?

Answer 8

yes it should be :-)

Answer 9

I dont know...

Answer 10

22=713x+437y
22=23*31x+23*19y

31x=a
19y=b
a+b=22
a=22-b
31x=22-19y

- for what integers x,y can you make this equale ?

Answer 11

You tell me :-)

Answer 12

I am more and more confident that it has no solutions

Answer 13

Hope thats right. I wrote that in my exam

Answer 14

Euclids algorith only work with coprime numbers so I dont think this should work

Answer 15

http://www.wolframalpha.com/input/?i=713x+%2B+437y+%3D+22+integer+solutions