Let m be a positive integer relatively prime to 10. Recall that the decimal expan- sion...

 

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Let m be a positive integer relatively prime to 10. Recall that the decimal expan- sion of 1/m is (purely) periodic, and its minimal period k is a divisor of ø(m). Prove that if k equals (m), then m must be a power of a prime p# 2, 5. Let m be a positive integer relatively prime to 10. Recall that the decimal expan- sion of 1/m is (purely) periodic, and its minimal period k is a divisor of ø(m). Prove that if k equals (m), then m must be a power of a prime p# 2, 5.