The Answer to the Question
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Here's the Solution to this Question
(a) Let us find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Since
we get that
Therefore, and hence
We conclude that 52 is the inverse of 19 modulo 141.
(b) Let us solve the congruence 19x ≡ 7 (mod 141),
Taking into account that we conclude that and thus
We conclude that the solution is of the form