Il existe 2 périodes de 89 chiffres pour n/179 en base 5.

Pour toutes les fractions de n/179 en base 5, la période de 1/179 revient alors 89 fois (en orange)

1/179=0,00032212112402311322443300202141343212440023440401112030140143420131422203341141021041311...

2/179=0,00114424230310123200442100404333241430430102431302224110330342340313344412232332042133122...

3/179=0,00202141343212440023440401112030140143420131422203341141021041311000322121124023113224433...

4/179=0,00234404011120301401434201314222033411410210413110003221211240231132244330020214134321244...

5/179=0,00322121124023113224433002021413432124400234404011120301401434201314222033411410210413110...

6/179=0,00404333241430430102431302224110330342340313344412232332042133122001144242303101232004421...

7/179=0,00442100404333241430430102431302224110330342340313344412232332042133122001144242303101232...

8/179=0,01024313022241103303423403133444122323320421331220011442423031012320044210040433324143043...

9/179=0,01112030140143420131422203341141021041311000322121124023113224433002021413432124400234404...

10/179=0,01144242303101232004421004043332414304301024313022241103303423403133444122323320421331220...

11/179=0,01232004421004043332414304301024313022241103303423403133444122323320421331220011442423031...

12/179=0,01314222033411410210413110003221211240231132244330020214134321244002344040111203014014342...

13/179=0,01401434201314222033411410210413110003221211240231132244330020214134321244002344040111203...

14/179=0,01434201314222033411410210413110003221211240231132244330020214134321244002344040111203014...

15/179=0,02021413432124400234404011120301401434201314222033411410210413110003221211240231132244330...

16/179=0,02104131100032212112402311322443300202141343212440023440401112030140143420131422203341141...

17/179=0,02141343212440023440401112030140143420131422203341141021041311000322121124023113224433002...

18/179=0,02224110330342340313344412232332042133122001144242303101232004421004043332414304301024313...

19/179=0,02311322443300202141343212440023440401112030140143420131422203341141021041311000322121124...

20/179=0,02344040111203014014342013142220334114102104131100032212112402311322443300202141343212440...

21/179=0,02431302224110330342340313344412232332042133122001144242303101232004421004043332414304301...

22/179=0,03014014342013142220334114102104131100032212112402311322443300202141343212440023440401112...

23/179=0,03101232004421004043332414304301024313022241103303423403133444122323320421331220011442423...

24/179=0,03133444122323320421331220011442423031012320044210040433324143043010243130222411033034234...

25/179=0,03221211240231132244330020214134321244002344040111203014014342013142220334114102104131100...

26/179=0,03303423403133444122323320421331220011442423031012320044210040433324143043010243130222411...

27/179=0,03341141021041311000322121124023113224433002021413432124400234404011120301401434201314222...

28/179=0,03423403133444122323320421331220011442423031012320044210040433324143043010243130222411033...

29/179=0,04011120301401434201314222033411410210413110003221211240231132244330020214134321244002344...

30/179=0,04043332414304301024313022241103303423403133444122323320421331220011442423031012320044210...

31/179=0,04131100032212112402311322443300202141343212440023440401112030140143420131422203341141021...

32/179=0,04213312200114424230310123200442100404333241430430102431302224110330342340313344412232332...

33/179=0,04301024313022241103303423403133444122323320421331220011442423031012320044210040433324143...

34/179=0,04333241430430102431302224110330342340313344412232332042133122001144242303101232004421004...

35/179=0,04421004043332414304301024313022241103303423403133444122323320421331220011442423031012320...

36/179=0,10003221211240231132244330020214134321244002344040111203014014342013142220334114102104131...

37/179=0,10040433324143043010243130222411033034234031334441223233204213312200114424230310123200442...

38/179=0,10123200442100404333241430430102431302224110330342340313344412232332042133122001144242303...

39/179=0,10210413110003221211240231132244330020214134321244002344040111203014014342013142220334114...

40/179=0,10243130222411033034234031334441223233204213312200114424230310123200442100404333241430430...

41/179=0,10330342340313344412232332042133122001144242303101232004421004043332414304301024313022241...

42/179=0,10413110003221211240231132244330020214134321244002344040111203014014342013142220334114102...

43/179=0,11000322121124023113224433002021413432124400234404011120301401434201314222033411410210413...

44/179=0,11033034234031334441223233204213312200114424230310123200442100404333241430430102431302224...

45/179=0,11120301401434201314222033411410210413110003221211240231132244330020214134321244002344040...

46/179=0,11203014014342013142220334114102104131100032212112402311322443300202141343212440023440401...

47/179=0,11240231132244330020214134321244002344040111203014014342013142220334114102104131100032212...

48/179=0,11322443300202141343212440023440401112030140143420131422203341141021041311000322121124023...

49/179=0,11410210413110003221211240231132244330020214134321244002344040111203014014342013142220334...

50/179=0,11442423031012320044210040433324143043010243130222411033034234031334441223233204213312200...

51/179=0,12030140143420131422203341141021041311000322121124023113224433002021413432124400234404011...

52/179=0,12112402311322443300202141343212440023440401112030140143420131422203341141021041311000322...

53/179=0,12200114424230310123200442100404333241430430102431302224110330342340313344412232332042133...

54/179=0,12232332042133122001144242303101232004421004043332414304301024313022241103303423403133444...

55/179=0,12320044210040433324143043010243130222411033034234031334441223233204213312200114424230310...

56/179=0,12402311322443300202141343212440023440401112030140143420131422203341141021041311000322121...

57/179=0,12440023440401112030140143420131422203341141021041311000322121124023113224433002021413432...

58/179=0,13022241103303423403133444122323320421331220011442423031012320044210040433324143043010243...

59/179=0,13110003221211240231132244330020214134321244002344040111203014014342013142220334114102104...

60/179=0,13142220334114102104131100032212112402311322443300202141343212440023440401112030140143420...

61/179=0,13224433002021413432124400234404011120301401434201314222033411410210413110003221211240231...

62/179=0,13312200114424230310123200442100404333241430430102431302224110330342340313344412232332042...

63/179=0,13344412232332042133122001144242303101232004421004043332414304301024313022241103303423403...

64/179=0,13432124400234404011120301401434201314222033411410210413110003221211240231132244330020214...

65/179=0,14014342013142220334114102104131100032212112402311322443300202141343212440023440401112030...

66/179=0,14102104131100032212112402311322443300202141343212440023440401112030140143420131422203341...

67/179=0,14134321244002344040111203014014342013142220334114102104131100032212112402311322443300202...

68/179=0,14222033411410210413110003221211240231132244330020214134321244002344040111203014014342013...

69/179=0,14304301024313022241103303423403133444122323320421331220011442423031012320044210040433324...

70/179=0,14342013142220334114102104131100032212112402311322443300202141343212440023440401112030140...

71/179=0,14424230310123200442100404333241430430102431302224110330342340313344412232332042133122001...

72/179=0,20011442423031012320044210040433324143043010243130222411033034234031334441223233204213312...

73/179=0,20044210040433324143043010243130222411033034234031334441223233204213312200114424230310123...

74/179=0,20131422203341141021041311000322121124023113224433002021413432124400234404011120301401434...

75/179=0,20214134321244002344040111203014014342013142220334114102104131100032212112402311322443300...

76/179=0,20301401434201314222033411410210413110003221211240231132244330020214134321244002344040111...

77/179=0,20334114102104131100032212112402311322443300202141343212440023440401112030140143420131422...

78/179=0,20421331220011442423031012320044210040433324143043010243130222411033034234031334441223233...

79/179=0,21004043332414304301024313022241103303423403133444122323320421331220011442423031012320044...

80/179=0,21041311000322121124023113224433002021413432124400234404011120301401434201314222033411410...

81/179=0,21124023113224433002021413432124400234404011120301401434201314222033411410210413110003221...

82/179=0,21211240231132244330020214134321244002344040111203014014342013142220334114102104131100032...

83/179=0,21244002344040111203014014342013142220334114102104131100032212112402311322443300202141343...

84/179=0,21331220011442423031012320044210040433324143043010243130222411033034234031334441223233204...

85/179=0,21413432124400234404011120301401434201314222033411410210413110003221211240231132244330020...

86/179=0,22001144242303101232004421004043332414304301024313022241103303423403133444122323320421331...

87/179=0,22033411410210413110003221211240231132244330020214134321244002344040111203014014342013142...

88/179=0,22121124023113224433002021413432124400234404011120301401434201314222033411410210413110003...

89/179=0,22203341141021041311000322121124023113224433002021413432124400234404011120301401434201314...

90/179=0,22241103303423403133444122323320421331220011442423031012320044210040433324143043010243130...

91/179=0,22323320421331220011442423031012320044210040433324143043010243130222411033034234031334441...

92/179=0,22411033034234031334441223233204213312200114424230310123200442100404333241430430102431302...

93/179=0,22443300202141343212440023440401112030140143420131422203341141021041311000322121124023113...

94/179=0,23031012320044210040433324143043010243130222411033034234031334441223233204213312200114424...

95/179=0,23113224433002021413432124400234404011120301401434201314222033411410210413110003221211240...

96/179=0,23200442100404333241430430102431302224110330342340313344412232332042133122001144242303101...

97/179=0,23233204213312200114424230310123200442100404333241430430102431302224110330342340313344412...

98/179=0,23320421331220011442423031012320044210040433324143043010243130222411033034234031334441223...

99/179=0,23403133444122323320421331220011442423031012320044210040433324143043010243130222411033034...

100/179=0,23440401112030140143420131422203341141021041311000322121124023113224433002021413432124400...

101/179=0,24023113224433002021413432124400234404011120301401434201314222033411410210413110003221211...

102/179=0,24110330342340313344412232332042133122001144242303101232004421004043332414304301024313022...

103/179=0,24143043010243130222411033034234031334441223233204213312200114424230310123200442100404333...

104/179=0,24230310123200442100404333241430430102431302224110330342340313344412232332042133122001144...

105/179=0,24313022241103303423403133444122323320421331220011442423031012320044210040433324143043010...

106/179=0,24400234404011120301401434201314222033411410210413110003221211240231132244330020214134321...

107/179=0,24433002021413432124400234404011120301401434201314222033411410210413110003221211240231132...

108/179=0,30020214134321244002344040111203014014342013142220334114102104131100032212112402311322443...

109/179=0,30102431302224110330342340313344412232332042133122001144242303101232004421004043332414304...

110/179=0,30140143420131422203341141021041311000322121124023113224433002021413432124400234404011120...

111/179=0,30222411033034234031334441223233204213312200114424230310123200442100404333241430430102431...

112/179=0,30310123200442100404333241430430102431302224110330342340313344412232332042133122001144242...

113/179=0,30342340313344412232332042133122001144242303101232004421004043332414304301024313022241103...

114/179=0,30430102431302224110330342340313344412232332042133122001144242303101232004421004043332414...

115/179=0,31012320044210040433324143043010243130222411033034234031334441223233204213312200114424230...

116/179=0,31100032212112402311322443300202141343212440023440401112030140143420131422203341141021041...

117/179=0,31132244330020214134321244002344040111203014014342013142220334114102104131100032212112402...

118/179=0,31220011442423031012320044210040433324143043010243130222411033034234031334441223233204213...

119/179=0,31302224110330342340313344412232332042133122001144242303101232004421004043332414304301024...

120/179=0,31334441223233204213312200114424230310123200442100404333241430430102431302224110330342340...

121/179=0,31422203341141021041311000322121124023113224433002021413432124400234404011120301401434201...

122/179=0,32004421004043332414304301024313022241103303423403133444122323320421331220011442423031012...

123/179=0,32042133122001144242303101232004421004043332414304301024313022241103303423403133444122323...

124/179=0,32124400234404011120301401434201314222033411410210413110003221211240231132244330020214134...

125/179=0,32212112402311322443300202141343212440023440401112030140143420131422203341141021041311000...

126/179=0,32244330020214134321244002344040111203014014342013142220334114102104131100032212112402311...

127/179=0,32332042133122001144242303101232004421004043332414304301024313022241103303423403133444122...

128/179=0,32414304301024313022241103303423403133444122323320421331220011442423031012320044210040433...

129/179=0,33002021413432124400234404011120301401434201314222033411410210413110003221211240231132244...

130/179=0,33034234031334441223233204213312200114424230310123200442100404333241430430102431302224110...

131/179=0,33122001144242303101232004421004043332414304301024313022241103303423403133444122323320421...

132/179=0,33204213312200114424230310123200442100404333241430430102431302224110330342340313344412232...

133/179=0,33241430430102431302224110330342340313344412232332042133122001144242303101232004421004043...

134/179=0,33324143043010243130222411033034234031334441223233204213312200114424230310123200442100404...

135/179=0,33411410210413110003221211240231132244330020214134321244002344040111203014014342013142220...

136/179=0,33444122323320421331220011442423031012320044210040433324143043010243130222411033034234031...

137/179=0,34031334441223233204213312200114424230310123200442100404333241430430102431302224110330342...

138/179=0,34114102104131100032212112402311322443300202141343212440023440401112030140143420131422203...

139/179=0,34201314222033411410210413110003221211240231132244330020214134321244002344040111203014014...

140/179=0,34234031334441223233204213312200114424230310123200442100404333241430430102431302224110330...

141/179=0,34321244002344040111203014014342013142220334114102104131100032212112402311322443300202141...

142/179=0,34404011120301401434201314222033411410210413110003221211240231132244330020214134321244002...

143/179=0,34441223233204213312200114424230310123200442100404333241430430102431302224110330342340313...

144/179=0,40023440401112030140143420131422203341141021041311000322121124023113224433002021413432124...

145/179=0,40111203014014342013142220334114102104131100032212112402311322443300202141343212440023440...

146/179=0,40143420131422203341141021041311000322121124023113224433002021413432124400234404011120301...

147/179=0,40231132244330020214134321244002344040111203014014342013142220334114102104131100032212112...

148/179=0,40313344412232332042133122001144242303101232004421004043332414304301024313022241103303423...

149/179=0,40401112030140143420131422203341141021041311000322121124023113224433002021413432124400234...

150/179=0,40433324143043010243130222411033034234031334441223233204213312200114424230310123200442100...

151/179=0,41021041311000322121124023113224433002021413432124400234404011120301401434201314222033411...

152/179=0,41103303423403133444122323320421331220011442423031012320044210040433324143043010243130222...

153/179=0,41141021041311000322121124023113224433002021413432124400234404011120301401434201314222033...

154/179=0,41223233204213312200114424230310123200442100404333241430430102431302224110330342340313344...

155/179=0,41311000322121124023113224433002021413432124400234404011120301401434201314222033411410210...

156/179=0,41343212440023440401112030140143420131422203341141021041311000322121124023113224433002021...

157/179=0,41430430102431302224110330342340313344412232332042133122001144242303101232004421004043332...

158/179=0,42013142220334114102104131100032212112402311322443300202141343212440023440401112030140143...

159/179=0,42100404333241430430102431302224110330342340313344412232332042133122001144242303101232004...

160/179=0,42133122001144242303101232004421004043332414304301024313022241103303423403133444122323320...

161/179=0,42220334114102104131100032212112402311322443300202141343212440023440401112030140143420131...

162/179=0,42303101232004421004043332414304301024313022241103303423403133444122323320421331220011442...

163/179=0,42340313344412232332042133122001144242303101232004421004043332414304301024313022241103303...

164/179=0,42423031012320044210040433324143043010243130222411033034234031334441223233204213312200114...

165/179=0,43010243130222411033034234031334441223233204213312200114424230310123200442100404333241430...

166/179=0,43043010243130222411033034234031334441223233204213312200114424230310123200442100404333241...

167/179=0,43130222411033034234031334441223233204213312200114424230310123200442100404333241430430102...

168/179=0,43212440023440401112030140143420131422203341141021041311000322121124023113224433002021413...

169/179=0,43300202141343212440023440401112030140143420131422203341141021041311000322121124023113224...

170/179=0,43332414304301024313022241103303423403133444122323320421331220011442423031012320044210040...

171/179=0,43420131422203341141021041311000322121124023113224433002021413432124400234404011120301401...

172/179=0,44002344040111203014014342013142220334114102104131100032212112402311322443300202141343212...

173/179=0,44040111203014014342013142220334114102104131100032212112402311322443300202141343212440023...

174/179=0,44122323320421331220011442423031012320044210040433324143043010243130222411033034234031334...

175/179=0,44210040433324143043010243130222411033034234031334441223233204213312200114424230310123200...

176/179=0,44242303101232004421004043332414304301024313022241103303423403133444122323320421331220011...

177/179=0,44330020214134321244002344040111203014014342013142220334114102104131100032212112402311322...

178/179=0,44412232332042133122001144242303101232004421004043332414304301024313022241103303423403133...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (89) est égal à 178 et donc au premier -1.