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Compute \({997}^{-1}\) modulo \(1000\). Express your answer as an integer from \(0\) to \(999\).

 Mar 28, 2021
 #1
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\(\frac{1}{997}\equiv x\pmod {1000}\)

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

 Mar 28, 2021

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