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   Periodic decimals coincidence?
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   Author  Topic: Periodic decimals coincidence?  (Read 373 times)
JocK
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Periodic decimals coincidence?  
« on: May 26th, 2006, 4:19pm »
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1/11 = 0. 0 9 0 9 0 9 ...  
  ------>  0+9 = 9
 
2/11 = 0. 1 8 1 8 1 8 ...  
  ------>  1+8 = 9
 
1/7 = 0. 142 857 142 857 142 857 ...
  ------>  142 + 857 = 999
 
2/7 = 0. 285 714 285 714 285 714 ...
  ------>  285+714 = 999
 
1/13 = 0. 076 923 076 923 076 923 ...
  ------>  076+923 = 999
 
2/13 = 0. 153 846 153 846 153 846 ...
 ------>  153+846 = 999
 
3/13 = 0. 230769 230769 230769 ...
  ------>  230+769 = 999
 
1/91 = 0. 010 989 010 989 010 989 ...
  ------>  010+989=999
 
1/73 = 0. 0136 9863 0136 9863 ...
  ------>  0136+9863 = 9999
 
1/17 = 0. 05882352 94117647 05882352 94117647...
  ------>  05882352+94117647 = 99999999
 
 
Coincidence..?  Huh  
 
   
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xy - y = x5 - y4 - y3 = 20; x>0, y>0.
Barukh
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Re: Periodic decimals coincidence?  
« Reply #1 on: May 27th, 2006, 4:29am »
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No.
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Eigenray
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Re: Periodic decimals coincidence?  
« Reply #2 on: May 27th, 2006, 3:50pm »
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A fraction a/n, with (10a, n)=1, has this property iff for some r>0, the order of 10 mod p has even part 2r for all primes p|n.
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