Question

1. Consider (x − 5) mod 12 ≡ 9 mod 12. What is the value of...

1. Consider (x − 5) mod 12 ≡ 9 mod 12. What is the value of x? [2 points]
2. Are any of these numbers equivalent in Z12: 5, 8, 19, -21, 17? [4 points]
3. Consider the following numbers: (i) 123456; (ii) 546777; (iii) 456734561883. For each the these numbers, answer the following questions. [12 points]
(a) Identify the check digit.[1 point]
(b) Does the number satisfy the checksum? [9 points]
(c) For the numbers that do not satisfy the checksum, change the value of the check digit so that the new number does satisfy the checksum.[2 points]
4. It is now Tuesday. What was the day of the week, 271 days ago? (Hint: Subtract 271.)[2 points]

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