Let m be a positive integer not divisible by 2 or 5. Prove that thedecimal expansion of the fraction 1/m is periodic with period equalto the order of 10 modulo m.

Let m be a positive integer not divisible by 2 or 5. We want to prove that the decimal expansion of…

Answered: Let m be a positive integer not…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 30E: 30. Prove that any positive integer is congruent to its units digit modulo .

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Let m be a positive integer not divisible by 2 or 5. Prove that the decimal expansion of the fraction 1/m is periodic with period equal to the order of 10 modulo m.