ax+by=c has a solution iff d|c .

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If (x°,y°) is one Solution of ax+by=c ,(a,b)=d then x1=x°-b/dt , y1=y°+a/dt is the general solution. If (x°,y°) is one Solution of ax+by=c ,(a,b)=d then x1=x°-b/dt , y1=y°+a/dt is the general solution.
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