Corollary 8.4.7 guarantees the existence of an inverse modulo n for an integer a when a and n are relatively prime. Use Euclid’s lemma to prove that the inverse is unique modulo n. In other words, show that if s and t are any two integers whose product with a is congruent to 1 modulo nm then s and t congruent to each other modulo n.
Any two integers whose product with is congruent to modulo are congruent to each other modulo .
are relatively prime.
Suppose are integers such that
Consider the quantity
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