Il existe 2 périodes de 86 chiffres pour n/173 en base 4.

Pour toutes les fractions de n/173 en base 4, la période de 1/173 revient alors 86 fois (en orange)

1/173=0,00011322310202002032003230300311101120302103332201102313133130133010303302223221303123...

2/173=0,00023311221010010130013121201222202301210213331002211232332320332021213211113103212312...

3/173=0,00101300131212012222023012102133310022112323323203320212132111131032123120002331122101...

4/173=0,00113223102020020320032303003111011203021033322011023131331301330103033022232213031230...

5/173=0,00131212012222023012102133310022112323323203320212132111131032123120002331122101001013...

6/173=0,00203200323030031110112030210333220110231313313013301030330222322130312300011322310202...

7/173=0,00221123233232033202121321111310321231200023311221010010130013121201222202301210213331...

8/173=0,00233112210100101300131212012222023012102133310022112323323203320212132111131032123120...

9/173=0,00311101120302103332201102313133130133010303302223221303123000113223102020020320032303...

10/173=0,00323030031110112030210333220110231313313013301030330222322130312300011322310202002032...

11/173=0,01001013001312120122220230121021333100221123233232033202121321111310321231200023311221...

12/173=0,01013001312120122220230121021333100221123233232033202121321111310321231200023311221010...

13/173=0,01030330222322130312300011322310202002032003230300311101120302103332201102313133130133...

14/173=0,01102313133130133010303302223221303123000113223102020020320032303003111011203021033322...

15/173=0,01120302103332201102313133130133010303302223221303123000113223102020020320032303003111...

16/173=0,01132231020200203200323030031110112030210333220110231313313013301030330222322130312300...

17/173=0,01210213331002211232332320332021213211113103212312000233112210100101300131212012222023...

18/173=0,01222202301210213331002211232332320332021213211113103212312000233112210100101300131212...

19/173=0,01300131212012222023012102133310022112323323203320212132111131032123120002331122101001...

20/173=0,01312120122220230121021333100221123233232033202121321111310321231200023311221010010130...

21/173=0,01330103033022232213031230001132231020200203200323030031110112030210333220110231313313...

22/173=0,02002032003230300311101120302103332201102313133130133010303302223221303123000113223102...

23/173=0,02020020320032303003111011203021033322011023131331301330103033022232213031230001132231...

24/173=0,02032003230300311101120302103332201102313133130133010303302223221303123000113223102020...

25/173=0,02103332201102313133130133010303302223221303123000113223102020020320032303003111011203...

26/173=0,02121321111310321231200023311221010010130013121201222202301210213331002211232332320332...

27/173=0,02133310022112323323203320212132111131032123120002331122101001013001312120122220230121...

28/173=0,02211232332320332021213211113103212312000233112210100101300131212012222023012102133310...

29/173=0,02223221303123000113223102020020320032303003111011203021033322011023131331301330103033...

30/173=0,02301210213331002211232332320332021213211113103212312000233112210100101300131212012222...

31/173=0,02313133130133010303302223221303123000113223102020020320032303003111011203021033322011...

32/173=0,02331122101001013001312120122220230121021333100221123233232033202121321111310321231200...

33/173=0,03003111011203021033322011023131331301330103033022232213031230001132231020200203200323...

34/173=0,03021033322011023131331301330103033022232213031230001132231020200203200323030031110112...

35/173=0,03033022232213031230001132231020200203200323030031110112030210333220110231313313013301...

36/173=0,03111011203021033322011023131331301330103033022232213031230001132231020200203200323030...

37/173=0,03123000113223102020020320032303003111011203021033322011023131331301330103033022232213...

38/173=0,03200323030031110112030210333220110231313313013301030330222322130312300011322310202002...

39/173=0,03212312000233112210100101300131212012222023012102133310022112323323203320212132111131...

40/173=0,03230300311101120302103332201102313133130133010303302223221303123000113223102020020320...

41/173=0,03302223221303123000113223102020020320032303003111011203021033322011023131331301330103...

42/173=0,03320212132111131032123120002331122101001013001312120122220230121021333100221123233232...

43/173=0,03332201102313133130133010303302223221303123000113223102020020320032303003111011203021...

44/173=0,10010130013121201222202301210213331002211232332320332021213211113103212312000233112210...

45/173=0,10022112323323203320212132111131032123120002331122101001013001312120122220230121021333...

46/173=0,10100101300131212012222023012102133310022112323323203320212132111131032123120002331122...

47/173=0,10112030210333220110231313313013301030330222322130312300011322310202002032003230300311...

48/173=0,10130013121201222202301210213331002211232332320332021213211113103212312000233112210100...

49/173=0,10202002032003230300311101120302103332201102313133130133010303302223221303123000113223...

50/173=0,10213331002211232332320332021213211113103212312000233112210100101300131212012222023012...

51/173=0,10231313313013301030330222322130312300011322310202002032003230300311101120302103332201...

52/173=0,10303302223221303123000113223102020020320032303003111011203021033322011023131331301330...

53/173=0,10321231200023311221010010130013121201222202301210213331002211232332320332021213211113...

54/173=0,10333220110231313313013301030330222322130312300011322310202002032003230300311101120302...

55/173=0,11011203021033322011023131331301330103033022232213031230001132231020200203200323030031...

56/173=0,11023131331301330103033022232213031230001132231020200203200323030031110112030210333220...

57/173=0,11101120302103332201102313133130133010303302223221303123000113223102020020320032303003...

58/173=0,11113103212312000233112210100101300131212012222023012102133310022112323323203320212132...

59/173=0,11131032123120002331122101001013001312120122220230121021333100221123233232033202121321...

60/173=0,11203021033322011023131331301330103033022232213031230001132231020200203200323030031110...

61/173=0,11221010010130013121201222202301210213331002211232332320332021213211113103212312000233...

62/173=0,11232332320332021213211113103212312000233112210100101300131212012222023012102133310022...

63/173=0,11310321231200023311221010010130013121201222202301210213331002211232332320332021213211...

64/173=0,11322310202002032003230300311101120302103332201102313133130133010303302223221303123000...

65/173=0,12000233112210100101300131212012222023012102133310022112323323203320212132111131032123...

66/173=0,12012222023012102133310022112323323203320212132111131032123120002331122101001013001312...

67/173=0,12030210333220110231313313013301030330222322130312300011322310202002032003230300311101...

68/173=0,12102133310022112323323203320212132111131032123120002331122101001013001312120122220230...

69/173=0,12120122220230121021333100221123233232033202121321111310321231200023311221010010130013...

70/173=0,12132111131032123120002331122101001013001312120122220230121021333100221123233232033202...

71/173=0,12210100101300131212012222023012102133310022112323323203320212132111131032123120002331...

72/173=0,12222023012102133310022112323323203320212132111131032123120002331122101001013001312120...

73/173=0,12300011322310202002032003230300311101120302103332201102313133130133010303302223221303...

74/173=0,12312000233112210100101300131212012222023012102133310022112323323203320212132111131032...

75/173=0,12323323203320212132111131032123120002331122101001013001312120122220230121021333100221...

76/173=0,13001312120122220230121021333100221123233232033202121321111310321231200023311221010010...

77/173=0,13013301030330222322130312300011322310202002032003230300311101120302103332201102313133...

78/173=0,13031230001132231020200203200323030031110112030210333220110231313313013301030330222322...

79/173=0,13103212312000233112210100101300131212012222023012102133310022112323323203320212132111...

80/173=0,13121201222202301210213331002211232332320332021213211113103212312000233112210100101300...

81/173=0,13133130133010303302223221303123000113223102020020320032303003111011203021033322011023...

82/173=0,13211113103212312000233112210100101300131212012222023012102133310022112323323203320212...

83/173=0,13223102020020320032303003111011203021033322011023131331301330103033022232213031230001...

84/173=0,13301030330222322130312300011322310202002032003230300311101120302103332201102313133130...

85/173=0,13313013301030330222322130312300011322310202002032003230300311101120302103332201102313...

86/173=0,13331002211232332320332021213211113103212312000233112210100101300131212012222023012102...

87/173=0,20002331122101001013001312120122220230121021333100221123233232033202121321111310321231...

88/173=0,20020320032303003111011203021033322011023131331301330103033022232213031230001132231020...

89/173=0,20032303003111011203021033322011023131331301330103033022232213031230001132231020200203...

90/173=0,20110231313313013301030330222322130312300011322310202002032003230300311101120302103332...

91/173=0,20122220230121021333100221123233232033202121321111310321231200023311221010010130013121...

92/173=0,20200203200323030031110112030210333220110231313313013301030330222322130312300011322310...

93/173=0,20212132111131032123120002331122101001013001312120122220230121021333100221123233232033...

94/173=0,20230121021333100221123233232033202121321111310321231200023311221010010130013121201222...

95/173=0,20302103332201102313133130133010303302223221303123000113223102020020320032303003111011...

96/173=0,20320032303003111011203021033322011023131331301330103033022232213031230001132231020200...

97/173=0,20332021213211113103212312000233112210100101300131212012222023012102133310022112323323...

98/173=0,21010010130013121201222202301210213331002211232332320332021213211113103212312000233112...

99/173=0,21021333100221123233232033202121321111310321231200023311221010010130013121201222202301...

100/173=0,21033322011023131331301330103033022232213031230001132231020200203200323030031110112030...

101/173=0,21111310321231200023311221010010130013121201222202301210213331002211232332320332021213...

102/173=0,21123233232033202121321111310321231200023311221010010130013121201222202301210213331002...

103/173=0,21201222202301210213331002211232332320332021213211113103212312000233112210100101300131...

104/173=0,21213211113103212312000233112210100101300131212012222023012102133310022112323323203320...

105/173=0,21231200023311221010010130013121201222202301210213331002211232332320332021213211113103...

106/173=0,21303123000113223102020020320032303003111011203021033322011023131331301330103033022232...

107/173=0,21321111310321231200023311221010010130013121201222202301210213331002211232332320332021...

108/173=0,21333100221123233232033202121321111310321231200023311221010010130013121201222202301210...

109/173=0,22011023131331301330103033022232213031230001132231020200203200323030031110112030210333...

110/173=0,22023012102133310022112323323203320212132111131032123120002331122101001013001312120122...

111/173=0,22101001013001312120122220230121021333100221123233232033202121321111310321231200023311...

112/173=0,22112323323203320212132111131032123120002331122101001013001312120122220230121021333100...

113/173=0,22130312300011322310202002032003230300311101120302103332201102313133130133010303302223...

114/173=0,22202301210213331002211232332320332021213211113103212312000233112210100101300131212012...

115/173=0,22220230121021333100221123233232033202121321111310321231200023311221010010130013121201...

116/173=0,22232213031230001132231020200203200323030031110112030210333220110231313313013301030330...

117/173=0,22310202002032003230300311101120302103332201102313133130133010303302223221303123000113...

118/173=0,22322130312300011322310202002032003230300311101120302103332201102313133130133010303302...

119/173=0,23000113223102020020320032303003111011203021033322011023131331301330103033022232213031...

120/173=0,23012102133310022112323323203320212132111131032123120002331122101001013001312120122220...

121/173=0,23030031110112030210333220110231313313013301030330222322130312300011322310202002032003...

122/173=0,23102020020320032303003111011203021033322011023131331301330103033022232213031230001132...

123/173=0,23120002331122101001013001312120122220230121021333100221123233232033202121321111310321...

124/173=0,23131331301330103033022232213031230001132231020200203200323030031110112030210333220110...

125/173=0,23203320212132111131032123120002331122101001013001312120122220230121021333100221123233...

126/173=0,23221303123000113223102020020320032303003111011203021033322011023131331301330103033022...

127/173=0,23233232033202121321111310321231200023311221010010130013121201222202301210213331002211...

128/173=0,23311221010010130013121201222202301210213331002211232332320332021213211113103212312000...

129/173=0,23323203320212132111131032123120002331122101001013001312120122220230121021333100221123...

130/173=0,30001132231020200203200323030031110112030210333220110231313313013301030330222322130312...

131/173=0,30013121201222202301210213331002211232332320332021213211113103212312000233112210100101...

132/173=0,30031110112030210333220110231313313013301030330222322130312300011322310202002032003230...

133/173=0,30103033022232213031230001132231020200203200323030031110112030210333220110231313313013...

134/173=0,30121021333100221123233232033202121321111310321231200023311221010010130013121201222202...

135/173=0,30133010303302223221303123000113223102020020320032303003111011203021033322011023131331...

136/173=0,30210333220110231313313013301030330222322130312300011322310202002032003230300311101120...

137/173=0,30222322130312300011322310202002032003230300311101120302103332201102313133130133010303...

138/173=0,30300311101120302103332201102313133130133010303302223221303123000113223102020020320032...

139/173=0,30312300011322310202002032003230300311101120302103332201102313133130133010303302223221...

140/173=0,30330222322130312300011322310202002032003230300311101120302103332201102313133130133010...

141/173=0,31002211232332320332021213211113103212312000233112210100101300131212012222023012102133...

142/173=0,31020200203200323030031110112030210333220110231313313013301030330222322130312300011322...

143/173=0,31032123120002331122101001013001312120122220230121021333100221123233232033202121321111...

144/173=0,31110112030210333220110231313313013301030330222322130312300011322310202002032003230300...

145/173=0,31122101001013001312120122220230121021333100221123233232033202121321111310321231200023...

146/173=0,31200023311221010010130013121201222202301210213331002211232332320332021213211113103212...

147/173=0,31212012222023012102133310022112323323203320212132111131032123120002331122101001013001...

148/173=0,31230001132231020200203200323030031110112030210333220110231313313013301030330222322130...

149/173=0,31301330103033022232213031230001132231020200203200323030031110112030210333220110231313...

150/173=0,31313313013301030330222322130312300011322310202002032003230300311101120302103332201102...

151/173=0,31331301330103033022232213031230001132231020200203200323030031110112030210333220110231...

152/173=0,32003230300311101120302103332201102313133130133010303302223221303123000113223102020020...

153/173=0,32021213211113103212312000233112210100101300131212012222023012102133310022112323323203...

154/173=0,32033202121321111310321231200023311221010010130013121201222202301210213331002211232332...

155/173=0,32111131032123120002331122101001013001312120122220230121021333100221123233232033202121...

156/173=0,32123120002331122101001013001312120122220230121021333100221123233232033202121321111310...

157/173=0,32201102313133130133010303302223221303123000113223102020020320032303003111011203021033...

158/173=0,32213031230001132231020200203200323030031110112030210333220110231313313013301030330222...

159/173=0,32231020200203200323030031110112030210333220110231313313013301030330222322130312300011...

160/173=0,32303003111011203021033322011023131331301330103033022232213031230001132231020200203200...

161/173=0,32320332021213211113103212312000233112210100101300131212012222023012102133310022112323...

162/173=0,32332320332021213211113103212312000233112210100101300131212012222023012102133310022112...

163/173=0,33010303302223221303123000113223102020020320032303003111011203021033322011023131331301...

164/173=0,33022232213031230001132231020200203200323030031110112030210333220110231313313013301030...

165/173=0,33100221123233232033202121321111310321231200023311221010010130013121201222202301210213...

166/173=0,33112210100101300131212012222023012102133310022112323323203320212132111131032123120002...

167/173=0,33130133010303302223221303123000113223102020020320032303003111011203021033322011023131...

168/173=0,33202121321111310321231200023311221010010130013121201222202301210213331002211232332320...

169/173=0,33220110231313313013301030330222322130312300011322310202002032003230300311101120302103...

170/173=0,33232033202121321111310321231200023311221010010130013121201222202301210213331002211232...

171/173=0,33310022112323323203320212132111131032123120002331122101001013001312120122220230121021...

172/173=0,33322011023131331301330103033022232213031230001132231020200203200323030031110112030210...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (86) est égal à 172 et donc au premier -1.