Il existe 2 périodes de 65 chiffres pour n/131 en base 5.

Pour toutes les fractions de n/131 en base 5, la période de 1/131 revient alors 65 fois (en orange)

1/131=0,00043411413342131003402022200241240301131443021211122101324321404...

2/131=0,00142323332234312012304044401033031102313441042422244203204143313...

3/131=0,00241240301131443021211122101324321404000434114133421310034020222...

4/131=0,00340202220024124030113144302121112210132432140400043411413342131...

5/131=0,00434114133421310034020222002412403011314430212111221013243214040...

6/131=0,01033031102313441042422244203204143313001423233322343120123040444...

7/131=0,01131443021211122101324321404000434114133421310034020222002412403...

8/131=0,01230404440103303110231344104242224420320414331300142323332234312...

9/131=0,01324321404000434114133421310034020222002412403011314430212111221...

10/131=0,01423233322343120123040444010330311023134410424222442032041433130...

11/131=0,02022200241240301131443021211122101324321404000434114133421310034...

12/131=0,02121112210132432140400043411413342131003402022200241240301131443...

13/131=0,02220024124030113144302121112210132432140400043411413342131003402...

14/131=0,02313441042422244203204143313001423233322343120123040444010330311...

15/131=0,02412403011314430212111221013243214040004341141334213100340202220...

16/131=0,03011314430212111221013243214040004341141334213100340202220024124...

17/131=0,03110231344104242224420320414331300142323332234312012304044401033...

18/131=0,03204143313001423233322343120123040444010330311023134410424222442...

19/131=0,03303110231344104242224420320414331300142323332234312012304044401...

20/131=0,03402022200241240301131443021211122101324321404000434114133421310...

21/131=0,04000434114133421310034020222002412403011314430212111221013243214...

22/131=0,04044401033031102313441042422244203204143313001423233322343120123...

23/131=0,04143313001423233322343120123040444010330311023134410424222442032...

24/131=0,04242224420320414331300142323332234312012304044401033031102313441...

25/131=0,04341141334213100340202220024124030113144302121112210132432140400...

26/131=0,04440103303110231344104242224420320414331300142323332234312012304...

27/131=0,10034020222002412403011314430212111221013243214040004341141334213...

28/131=0,10132432140400043411413342131003402022200241240301131443021211122...

29/131=0,10231344104242224420320414331300142323332234312012304044401033031...

30/131=0,10330311023134410424222442032041433130014232333223431201230404440...

31/131=0,10424222442032041433130014232333223431201230404440103303110231344...

32/131=0,11023134410424222442032041433130014232333223431201230404440103303...

33/131=0,11122101324321404000434114133421310034020222002412403011314430212...

34/131=0,11221013243214040004341141334213100340202220024124030113144302121...

35/131=0,11314430212111221013243214040004341141334213100340202220024124030...

36/131=0,11413342131003402022200241240301131443021211122101324321404000434...

37/131=0,12012304044401033031102313441042422244203204143313001423233322343...

38/131=0,12111221013243214040004341141334213100340202220024124030113144302...

39/131=0,12210132432140400043411413342131003402022200241240301131443021211...

40/131=0,12304044401033031102313441042422244203204143313001423233322343120...

41/131=0,12403011314430212111221013243214040004341141334213100340202220024...

42/131=0,13001423233322343120123040444010330311023134410424222442032041433...

43/131=0,13100340202220024124030113144302121112210132432140400043411413342...

44/131=0,13144302121112210132432140400043411413342131003402022200241240301...

45/131=0,13243214040004341141334213100340202220024124030113144302121112210...

46/131=0,13342131003402022200241240301131443021211122101324321404000434114...

47/131=0,13441042422244203204143313001423233322343120123040444010330311023...

48/131=0,14040004341141334213100340202220024124030113144302121112210132432...

49/131=0,14133421310034020222002412403011314430212111221013243214040004341...

50/131=0,14232333223431201230404440103303110231344104242224420320414331300...

51/131=0,14331300142323332234312012304044401033031102313441042422244203204...

52/131=0,14430212111221013243214040004341141334213100340202220024124030113...

53/131=0,20024124030113144302121112210132432140400043411413342131003402022...

54/131=0,20123040444010330311023134410424222442032041433130014232333223431...

55/131=0,20222002412403011314430212111221013243214040004341141334213100340...

56/131=0,20320414331300142323332234312012304044401033031102313441042422244...

57/131=0,20414331300142323332234312012304044401033031102313441042422244203...

58/131=0,21013243214040004341141334213100340202220024124030113144302121112...

59/131=0,21112210132432140400043411413342131003402022200241240301131443021...

60/131=0,21211122101324321404000434114133421310034020222002412403011314430...

61/131=0,21310034020222002412403011314430212111221013243214040004341141334...

62/131=0,21404000434114133421310034020222002412403011314430212111221013243...

63/131=0,22002412403011314430212111221013243214040004341141334213100340202...

64/131=0,22101324321404000434114133421310034020222002412403011314430212111...

65/131=0,22200241240301131443021211122101324321404000434114133421310034020...

66/131=0,22244203204143313001423233322343120123040444010330311023134410424...

67/131=0,22343120123040444010330311023134410424222442032041433130014232333...

68/131=0,22442032041433130014232333223431201230404440103303110231344104242...

69/131=0,23040444010330311023134410424222442032041433130014232333223431201...

70/131=0,23134410424222442032041433130014232333223431201230404440103303110...

71/131=0,23233322343120123040444010330311023134410424222442032041433130014...

72/131=0,23332234312012304044401033031102313441042422244203204143313001423...

73/131=0,23431201230404440103303110231344104242224420320414331300142323332...

74/131=0,24030113144302121112210132432140400043411413342131003402022200241...

75/131=0,24124030113144302121112210132432140400043411413342131003402022200...

76/131=0,24222442032041433130014232333223431201230404440103303110231344104...

77/131=0,24321404000434114133421310034020222002412403011314430212111221013...

78/131=0,24420320414331300142323332234312012304044401033031102313441042422...

79/131=0,30014232333223431201230404440103303110231344104242224420320414331...

80/131=0,30113144302121112210132432140400043411413342131003402022200241240...

81/131=0,30212111221013243214040004341141334213100340202220024124030113144...

82/131=0,30311023134410424222442032041433130014232333223431201230404440103...

83/131=0,30404440103303110231344104242224420320414331300142323332234312012...

84/131=0,31003402022200241240301131443021211122101324321404000434114133421...

85/131=0,31102313441042422244203204143313001423233322343120123040444010330...

86/131=0,31201230404440103303110231344104242224420320414331300142323332234...

87/131=0,31300142323332234312012304044401033031102313441042422244203204143...

88/131=0,31344104242224420320414331300142323332234312012304044401033031102...

89/131=0,31443021211122101324321404000434114133421310034020222002412403011...

90/131=0,32041433130014232333223431201230404440103303110231344104242224420...

91/131=0,32140400043411413342131003402022200241240301131443021211122101324...

92/131=0,32234312012304044401033031102313441042422244203204143313001423233...

93/131=0,32333223431201230404440103303110231344104242224420320414331300142...

94/131=0,32432140400043411413342131003402022200241240301131443021211122101...

95/131=0,33031102313441042422244203204143313001423233322343120123040444010...

96/131=0,33130014232333223431201230404440103303110231344104242224420320414...

97/131=0,33223431201230404440103303110231344104242224420320414331300142323...

98/131=0,33322343120123040444010330311023134410424222442032041433130014232...

99/131=0,33421310034020222002412403011314430212111221013243214040004341141...

100/131=0,34020222002412403011314430212111221013243214040004341141334213100...

101/131=0,34114133421310034020222002412403011314430212111221013243214040004...

102/131=0,34213100340202220024124030113144302121112210132432140400043411413...

103/131=0,34312012304044401033031102313441042422244203204143313001423233322...

104/131=0,34410424222442032041433130014232333223431201230404440103303110231...

105/131=0,40004341141334213100340202220024124030113144302121112210132432140...

106/131=0,40103303110231344104242224420320414331300142323332234312012304044...

107/131=0,40202220024124030113144302121112210132432140400043411413342131003...

108/131=0,40301131443021211122101324321404000434114133421310034020222002412...

109/131=0,40400043411413342131003402022200241240301131443021211122101324321...

110/131=0,40444010330311023134410424222442032041433130014232333223431201230...

111/131=0,41042422244203204143313001423233322343120123040444010330311023134...

112/131=0,41141334213100340202220024124030113144302121112210132432140400043...

113/131=0,41240301131443021211122101324321404000434114133421310034020222002...

114/131=0,41334213100340202220024124030113144302121112210132432140400043411...

115/131=0,41433130014232333223431201230404440103303110231344104242224420320...

116/131=0,42032041433130014232333223431201230404440103303110231344104242224...

117/131=0,42131003402022200241240301131443021211122101324321404000434114133...

118/131=0,42224420320414331300142323332234312012304044401033031102313441042...

119/131=0,42323332234312012304044401033031102313441042422244203204143313001...

120/131=0,42422244203204143313001423233322343120123040444010330311023134410...

121/131=0,43021211122101324321404000434114133421310034020222002412403011314...

122/131=0,43120123040444010330311023134410424222442032041433130014232333223...

123/131=0,43214040004341141334213100340202220024124030113144302121112210132...

124/131=0,43313001423233322343120123040444010330311023134410424222442032041...

125/131=0,43411413342131003402022200241240301131443021211122101324321404000...

126/131=0,44010330311023134410424222442032041433130014232333223431201230404...

127/131=0,44104242224420320414331300142323332234312012304044401033031102313...

128/131=0,44203204143313001423233322343120123040444010330311023134410424222...

129/131=0,44302121112210132432140400043411413342131003402022200241240301131...

130/131=0,44401033031102313441042422244203204143313001423233322343120123040...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (65) est égal à 130 et donc au premier -1.