Il existe 2 périodes de 83 chiffres pour n/167 en base 2.

Pour toutes les fractions de n/167 en base 2, la période de 1/167 revient alors 83 fois (en orange)

1/167=0,00000001100010000110111001011111000010101011101100000100100110010100101100011101001...

2/167=0,00000011000100001101110010111110000101010111011000001001001100101001011000111010010...

3/167=0,00000100100110010100101100011101001000000011000100001101110010111110000101010111011...

4/167=0,00000110001000011011100101111100001010101110110000010010011001010010110001110100100...

5/167=0,00000111101010100010011111011011001101011010011100010110111111100111011110010001101...

6/167=0,00001001001100101001011000111010010000000110001000011011100101111100001010101110110...

7/167=0,00001010101110110000010010011001010010110001110100100000001100010000110111001011111...

8/167=0,00001100010000110111001011111000010101011101100000100100110010100101100011101001000...

9/167=0,00001101110010111110000101010111011000001001001100101001011000111010010000000110001...

10/167=0,00001111010101000100111110110110011010110100111000101101111111001110111100100011010...

11/167=0,00010000110111001011111000010101011101100000100100110010100101100011101001000000011...

12/167=0,00010010011001010010110001110100100000001100010000110111001011111000010101011101100...

13/167=0,00010011111011011001101011010011100010110111111100111011110010001101000001111010101...

14/167=0,00010101011101100000100100110010100101100011101001000000011000100001101110010111110...

15/167=0,00010110111111100111011110010001101000001111010101000100111110110110011010110100111...

16/167=0,00011000100001101110010111110000101010111011000001001001100101001011000111010010000...

17/167=0,00011010000011110101010001001111101101100110101101001110001011011111110011101111001...

18/167=0,00011011100101111100001010101110110000010010011001010010110001110100100000001100010...

19/167=0,00011101001000000011000100001101110010111110000101010111011000001001001100101001011...

20/167=0,00011110101010001001111101101100110101101001110001011011111110011101111001000110100...

21/167=0,00100000001100010000110111001011111000010101011101100000100100110010100101100011101...

22/167=0,00100001101110010111110000101010111011000001001001100101001011000111010010000000110...

23/167=0,00100011010000011110101010001001111101101100110101101001110001011011111110011101111...

24/167=0,00100100110010100101100011101001000000011000100001101110010111110000101010111011000...

25/167=0,00100110010100101100011101001000000011000100001101110010111110000101010111011000001...

26/167=0,00100111110110110011010110100111000101101111111001110111100100011010000011110101010...

27/167=0,00101001011000111010010000000110001000011011100101111100001010101110110000010010011...

28/167=0,00101010111011000001001001100101001011000111010010000000110001000011011100101111100...

29/167=0,00101100011101001000000011000100001101110010111110000101010111011000001001001100101...

30/167=0,00101101111111001110111100100011010000011110101010001001111101101100110101101001110...

31/167=0,00101111100001010101110110000010010011001010010110001110100100000001100010000110111...

32/167=0,00110001000011011100101111100001010101110110000010010011001010010110001110100100000...

33/167=0,00110010100101100011101001000000011000100001101110010111110000101010111011000001001...

34/167=0,00110100000111101010100010011111011011001101011010011100010110111111100111011110010...

35/167=0,00110101101001110001011011111110011101111001000110100000111101010100010011111011011...

36/167=0,00110111001011111000010101011101100000100100110010100101100011101001000000011000100...

37/167=0,00111000101101111111001110111100100011010000011110101010001001111101101100110101101...

38/167=0,00111010010000000110001000011011100101111100001010101110110000010010011001010010110...

39/167=0,00111011110010001101000001111010101000100111110110110011010110100111000101101111111...

40/167=0,00111101010100010011111011011001101011010011100010110111111100111011110010001101000...

41/167=0,00111110110110011010110100111000101101111111001110111100100011010000011110101010001...

42/167=0,01000000011000100001101110010111110000101010111011000001001001100101001011000111010...

43/167=0,01000001111010101000100111110110110011010110100111000101101111111001110111100100011...

44/167=0,01000011011100101111100001010101110110000010010011001010010110001110100100000001100...

45/167=0,01000100111110110110011010110100111000101101111111001110111100100011010000011110101...

46/167=0,01000110100000111101010100010011111011011001101011010011100010110111111100111011110...

47/167=0,01001000000011000100001101110010111110000101010111011000001001001100101001011000111...

48/167=0,01001001100101001011000111010010000000110001000011011100101111100001010101110110000...

49/167=0,01001011000111010010000000110001000011011100101111100001010101110110000010010011001...

50/167=0,01001100101001011000111010010000000110001000011011100101111100001010101110110000010...

51/167=0,01001110001011011111110011101111001000110100000111101010100010011111011011001101011...

52/167=0,01001111101101100110101101001110001011011111110011101111001000110100000111101010100...

53/167=0,01010001001111101101100110101101001110001011011111110011101111001000110100000111101...

54/167=0,01010010110001110100100000001100010000110111001011111000010101011101100000100100110...

55/167=0,01010100010011111011011001101011010011100010110111111100111011110010001101000001111...

56/167=0,01010101110110000010010011001010010110001110100100000001100010000110111001011111000...

57/167=0,01010111011000001001001100101001011000111010010000000110001000011011100101111100001...

58/167=0,01011000111010010000000110001000011011100101111100001010101110110000010010011001010...

59/167=0,01011010011100010110111111100111011110010001101000001111010101000100111110110110011...

60/167=0,01011011111110011101111001000110100000111101010100010011111011011001101011010011100...

61/167=0,01011101100000100100110010100101100011101001000000011000100001101110010111110000101...

62/167=0,01011111000010101011101100000100100110010100101100011101001000000011000100001101110...

63/167=0,01100000100100110010100101100011101001000000011000100001101110010111110000101010111...

64/167=0,01100010000110111001011111000010101011101100000100100110010100101100011101001000000...

65/167=0,01100011101001000000011000100001101110010111110000101010111011000001001001100101001...

66/167=0,01100101001011000111010010000000110001000011011100101111100001010101110110000010010...

67/167=0,01100110101101001110001011011111110011101111001000110100000111101010100010011111011...

68/167=0,01101000001111010101000100111110110110011010110100111000101101111111001110111100100...

69/167=0,01101001110001011011111110011101111001000110100000111101010100010011111011011001101...

70/167=0,01101011010011100010110111111100111011110010001101000001111010101000100111110110110...

71/167=0,01101100110101101001110001011011111110011101111001000110100000111101010100010011111...

72/167=0,01101110010111110000101010111011000001001001100101001011000111010010000000110001000...

73/167=0,01101111111001110111100100011010000011110101010001001111101101100110101101001110001...

74/167=0,01110001011011111110011101111001000110100000111101010100010011111011011001101011010...

75/167=0,01110010111110000101010111011000001001001100101001011000111010010000000110001000011...

76/167=0,01110100100000001100010000110111001011111000010101011101100000100100110010100101100...

77/167=0,01110110000010010011001010010110001110100100000001100010000110111001011111000010101...

78/167=0,01110111100100011010000011110101010001001111101101100110101101001110001011011111110...

79/167=0,01111001000110100000111101010100010011111011011001101011010011100010110111111100111...

80/167=0,01111010101000100111110110110011010110100111000101101111111001110111100100011010000...

81/167=0,01111100001010101110110000010010011001010010110001110100100000001100010000110111001...

82/167=0,01111101101100110101101001110001011011111110011101111001000110100000111101010100010...

83/167=0,01111111001110111100100011010000011110101010001001111101101100110101101001110001011...

84/167=0,10000000110001000011011100101111100001010101110110000010010011001010010110001110100...

85/167=0,10000010010011001010010110001110100100000001100010000110111001011111000010101011101...

86/167=0,10000011110101010001001111101101100110101101001110001011011111110011101111001000110...

87/167=0,10000101010111011000001001001100101001011000111010010000000110001000011011100101111...

88/167=0,10000110111001011111000010101011101100000100100110010100101100011101001000000011000...

89/167=0,10001000011011100101111100001010101110110000010010011001010010110001110100100000001...

90/167=0,10001001111101101100110101101001110001011011111110011101111001000110100000111101010...

91/167=0,10001011011111110011101111001000110100000111101010100010011111011011001101011010011...

92/167=0,10001101000001111010101000100111110110110011010110100111000101101111111001110111100...

93/167=0,10001110100100000001100010000110111001011111000010101011101100000100100110010100101...

94/167=0,10010000000110001000011011100101111100001010101110110000010010011001010010110001110...

95/167=0,10010001101000001111010101000100111110110110011010110100111000101101111111001110111...

96/167=0,10010011001010010110001110100100000001100010000110111001011111000010101011101100000...

97/167=0,10010100101100011101001000000011000100001101110010111110000101010111011000001001001...

98/167=0,10010110001110100100000001100010000110111001011111000010101011101100000100100110010...

99/167=0,10010111110000101010111011000001001001100101001011000111010010000000110001000011011...

100/167=0,10011001010010110001110100100000001100010000110111001011111000010101011101100000100...

101/167=0,10011010110100111000101101111111001110111100100011010000011110101010001001111101101...

102/167=0,10011100010110111111100111011110010001101000001111010101000100111110110110011010110...

103/167=0,10011101111001000110100000111101010100010011111011011001101011010011100010110111111...

104/167=0,10011111011011001101011010011100010110111111100111011110010001101000001111010101000...

105/167=0,10100000111101010100010011111011011001101011010011100010110111111100111011110010001...

106/167=0,10100010011111011011001101011010011100010110111111100111011110010001101000001111010...

107/167=0,10100100000001100010000110111001011111000010101011101100000100100110010100101100011...

108/167=0,10100101100011101001000000011000100001101110010111110000101010111011000001001001100...

109/167=0,10100111000101101111111001110111100100011010000011110101010001001111101101100110101...

110/167=0,10101000100111110110110011010110100111000101101111111001110111100100011010000011110...

111/167=0,10101010001001111101101100110101101001110001011011111110011101111001000110100000111...

112/167=0,10101011101100000100100110010100101100011101001000000011000100001101110010111110000...

113/167=0,10101101001110001011011111110011101111001000110100000111101010100010011111011011001...

114/167=0,10101110110000010010011001010010110001110100100000001100010000110111001011111000010...

115/167=0,10110000010010011001010010110001110100100000001100010000110111001011111000010101011...

116/167=0,10110001110100100000001100010000110111001011111000010101011101100000100100110010100...

117/167=0,10110011010110100111000101101111111001110111100100011010000011110101010001001111101...

118/167=0,10110100111000101101111111001110111100100011010000011110101010001001111101101100110...

119/167=0,10110110011010110100111000101101111111001110111100100011010000011110101010001001111...

120/167=0,10110111111100111011110010001101000001111010101000100111110110110011010110100111000...

121/167=0,10111001011111000010101011101100000100100110010100101100011101001000000011000100001...

122/167=0,10111011000001001001100101001011000111010010000000110001000011011100101111100001010...

123/167=0,10111100100011010000011110101010001001111101101100110101101001110001011011111110011...

124/167=0,10111110000101010111011000001001001100101001011000111010010000000110001000011011100...

125/167=0,10111111100111011110010001101000001111010101000100111110110110011010110100111000101...

126/167=0,11000001001001100101001011000111010010000000110001000011011100101111100001010101110...

127/167=0,11000010101011101100000100100110010100101100011101001000000011000100001101110010111...

128/167=0,11000100001101110010111110000101010111011000001001001100101001011000111010010000000...

129/167=0,11000101101111111001110111100100011010000011110101010001001111101101100110101101001...

130/167=0,11000111010010000000110001000011011100101111100001010101110110000010010011001010010...

131/167=0,11001000110100000111101010100010011111011011001101011010011100010110111111100111011...

132/167=0,11001010010110001110100100000001100010000110111001011111000010101011101100000100100...

133/167=0,11001011111000010101011101100000100100110010100101100011101001000000011000100001101...

134/167=0,11001101011010011100010110111111100111011110010001101000001111010101000100111110110...

135/167=0,11001110111100100011010000011110101010001001111101101100110101101001110001011011111...

136/167=0,11010000011110101010001001111101101100110101101001110001011011111110011101111001000...

137/167=0,11010010000000110001000011011100101111100001010101110110000010010011001010010110001...

138/167=0,11010011100010110111111100111011110010001101000001111010101000100111110110110011010...

139/167=0,11010101000100111110110110011010110100111000101101111111001110111100100011010000011...

140/167=0,11010110100111000101101111111001110111100100011010000011110101010001001111101101100...

141/167=0,11011000001001001100101001011000111010010000000110001000011011100101111100001010101...

142/167=0,11011001101011010011100010110111111100111011110010001101000001111010101000100111110...

143/167=0,11011011001101011010011100010110111111100111011110010001101000001111010101000100111...

144/167=0,11011100101111100001010101110110000010010011001010010110001110100100000001100010000...

145/167=0,11011110010001101000001111010101000100111110110110011010110100111000101101111111001...

146/167=0,11011111110011101111001000110100000111101010100010011111011011001101011010011100010...

147/167=0,11100001010101110110000010010011001010010110001110100100000001100010000110111001011...

148/167=0,11100010110111111100111011110010001101000001111010101000100111110110110011010110100...

149/167=0,11100100011010000011110101010001001111101101100110101101001110001011011111110011101...

150/167=0,11100101111100001010101110110000010010011001010010110001110100100000001100010000110...

151/167=0,11100111011110010001101000001111010101000100111110110110011010110100111000101101111...

152/167=0,11101001000000011000100001101110010111110000101010111011000001001001100101001011000...

153/167=0,11101010100010011111011011001101011010011100010110111111100111011110010001101000001...

154/167=0,11101100000100100110010100101100011101001000000011000100001101110010111110000101010...

155/167=0,11101101100110101101001110001011011111110011101111001000110100000111101010100010011...

156/167=0,11101111001000110100000111101010100010011111011011001101011010011100010110111111100...

157/167=0,11110000101010111011000001001001100101001011000111010010000000110001000011011100101...

158/167=0,11110010001101000001111010101000100111110110110011010110100111000101101111111001110...

159/167=0,11110011101111001000110100000111101010100010011111011011001101011010011100010110111...

160/167=0,11110101010001001111101101100110101101001110001011011111110011101111001000110100000...

161/167=0,11110110110011010110100111000101101111111001110111100100011010000011110101010001001...

162/167=0,11111000010101011101100000100100110010100101100011101001000000011000100001101110010...

163/167=0,11111001110111100100011010000011110101010001001111101101100110101101001110001011011...

164/167=0,11111011011001101011010011100010110111111100111011110010001101000001111010101000100...

165/167=0,11111100111011110010001101000001111010101000100111110110110011010110100111000101101...

166/167=0,11111110011101111001000110100000111101010100010011111011011001101011010011100010110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (83) est égal à 166 et donc au premier -1.