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What is the unique three-digit positive integer satisfying 100x = 11 (mod 997)

 Jun 4, 2022
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gcd(100, 997) = 1. The congruence is solvable and it has unique solution.


100x≡11(mod997)


⟹1000x≡110(mod997)


⟹3x≡110(mod997)


⟹999x≡36630(mod997)


⟹2x≡738(mod997)


⟹998x≡499×738(mod997)


⟹x≡369(mod997)


369 is the required unique 3-digit positive integer.

 Jun 5, 2022

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