Efficiently finding congruencies All variables are integers with a value somewhere between 0-99, inclusive.
ax + b % 100 = n and you are given everything except x.
Example: 65x + 6 is congruent with 81 mod 100.
I am trying to find a way to determine the potentially valid values of x without resorting to brute force.  Is there a known method more efficient than brute force for a problem like this?  If so, can anyone explain how the congruencies are found and/or possibly point me in the direction of any tutorials, books, or videos?
$65x+6\equiv81\bmod100\iff65x\equiv75\bmod100\iff$
$13x\equiv15\bmod20\iff7x\equiv5\bmod20\iff x\equiv3\times7x\equiv3\times5=15\bmod20$
$65x+6\equiv81\bmod100\iff65x\equiv75\bmod100\iff$
$13x\equiv15\bmod20\iff7x\equiv5\bmod20\iff x\equiv3\times7x\equiv3\times5=15\bmod20$