Inverses With Linear Combinations
What is the inverse \((\text{mod } 25)\) of \(32\)?
Reminder: Your answer must be an integer in the interval \([0,25)\).
Since \(1 = 9\cdot 25 + (-7)\cdot 32\), it follows that \(-7\) is an inverse of \(32 (\text{mod } 25)\), and therefore so is \(rem(-7,25) = 18\).