2. Let meN and a € Z. (a) If ged(a,m) = 1, then Bézout's lemma gives the existence of integers x and y such that ax + my = 1. Prove that a+mZ is the multiplicative inverse of a +mZ. (b) Determine the least nonnegative integer representative for (11+163Z)-¹ by expressing 1 as a linear combination of 11 and 163 (using the extended Euclidean algorithm).

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