- #1
rayman123
- 152
- 0
Homework Statement
Solve [tex]57x+4y=2[/tex]
Homework Equations
I use the equation [tex]57x+4y=1[/tex] find
[tex]gcd(57,4)[/tex] as follows
[tex]57=14\cdot 4+1[/tex] then [tex]gcd(57,4)=1[/tex] and
[tex]1=57-4\cdot 14[/tex] so the particular solution to my first equation is
[tex]x_{0}=2[/tex]*and [tex]y_{0}=-28[/tex]
Wolfram says it is correct but I am not sure if the Euclidean algorithm is computed correctly
If for example I have now
[tex]37x+32y=3[/tex]
is the computation of gcd(37,32) correct?
[tex]37=32\cdot 1+5[/tex]
[tex]32=5\cdot 6+2[/tex]
[tex]5=2\cdot 2+1[/tex]
but now I don't know how to find the linear combination of these...to obtain the particular solution. Please help