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5-digit period (Posted on 2011-12-16) Difficulty: 3 of 5
What are two primes p > 0 for which 1/p has a purely periodic decimal expansion with a period 5 digits long?

Source: California math competition 2001

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (3 votes)

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Solution Answer | Comment 1 of 3

For the period to be 5 digits long, it has to divide 99999. The factorization of 99999 is 3^2*41*271. 1/3 has a period of 1, but 1/41 and 1/271 have a period of 5. Therefore, the two primes are 41 and 271.

 


  Posted by Math Man on 2011-12-16 10:25:24
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