I have an equation as follows: $27217 = 5s $ mod $42547$
Using this website https://www.dcode.fr/modular-equation-solver, the correct result for s is 39481 as shown below however it does not list what steps are being done.
Solving modular equation using dCode
How would one go about to find the value of s in this modular equation?
We must have that $$5s-27217=42547t$$for some integer $t$. Therefore $$5(s-5443-8509t)=2t+2$$thereby dividing $27217$ and $42547$ over $5$. By defining $q=5-5443-8509t$ we obtain the following easy-to-solve equation$$5q=2t+2$$which has an answer $q=2$ and $t=4$ yielding to $$s=39481$$therefore all the answers can be found as follows $$s=39481+42547k\quad,\quad k\in \Bbb Z$$