Question

Find the general solution of the congruence
$98x-1\equiv 0(\text{mod}.139)$.

Answer 1

The congruence $98x-1=0$($\text{mod}$ $139$)

means that $98x-1$ is divisible by $139$

If $y$ is the quotient, then $98x-1=139y$, or $98x-139y=1$

If $\frac{139}{98}$ is converted into a continued fraction the convergent just preceding the fraction is $\frac{61}{43}$.

Hence, the general solution of the equation is

$x=61+139t,y=43+98t$