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# Modular Arithmetic Inverses/Congruences Questions

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1. What is the smallest integer $$n$$, greater than $$1$$, such that n^(-1) (mod 130) and n^(-1) (mod 231) are both defined?

2. What is the unique three-digit positive integer $$x$$ satisfying $$100x\equiv1 (mod 997)$$

Aug 2, 2018

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2)  100x mod 997 = 1

100 x - 997 floor((100 x)/997) = 1

x = 668

Aug 3, 2018