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**Unformatted text preview: **When b = 1 the equivalence class is called the multiplicative inverse in ℤ Examples: What about SYSTEMS of linear congruence equations? ( 29 ( 29 ( 29 1 1 1 2 2 2 mod mod ... mod k a x b m ≡ ≡ ≡ When does it have a solution? Why can we reduce this to a system where all the moduli are relatively prime? Early Chinese contributions to this type of problem occur in the literature as early as the first century AD – so the method of solution is called the Chinese Remainder Theorem. The Chinese Remainder Theorem Example Example:...

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