+25 Compute \({997}^{-1}\) modulo \(1000\). Express your answer as an integer from \(0\) to \(999\).
+150 \(\frac{1}{997}\equiv x\pmod {1000}\)
997|1000(1000-a)+1
(1000-3)|(1000)(1000-a)+1
last 3 digits from (1000)1000-a+1 = 001.
then, last 3 digits from 1000-3 is 001 too.
chance : (1000-3)*333.
=> 997*333.
x=333
