- #1

rayman123

- 152

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## 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 dont know how to find the linear combination of these...to obtain the particular solution. Please help