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Prove the following statements: (a) If gcd(a, n)=1, then the integers c, c+a, c+2 a, c+3 a, …, c+(n-1) a form a complete set of residues modulo n for any c. (b) Any n consecutive integers form a complete set of residues modulo n. [Hint: Use part (a).] (c) The product of any set of n consecutive integers is divisible by n. | Numerade
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