Question

31. Consider the repeating decimals 428571428571..., 11 .4545..., etc. These repeating decimals have period 6 and 2, respectively. In general, let p be any prime other than 2 or 5. We wish to derive an analogous result. a. Prove that the remainders obtained when you do the long division form a subgroup of Zp. b. Deduce that the period of the repeating decimal is a divi- sor of p 1.

Answer 1

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