210 MR. G. T. BENNETT ON THE RESIDUES OF POWERS OF NUMBERS 
therefore 
and 
therefore 
t = 20, 
2? is divided by 2® 
T — 2. 
2. 4. 8. 16. 32. 64. 28. 56. 12. 24. 48. 96. 92. 84. 68. 36. 72. 44. 88. 76. 52, 
the points indicating the period. 
Powers of 5 mod 1000 = 2® . 5®. 
therefore 
therefore 
5 has exp 2 mod 2®, 
t = 2, 
5^ is divided by 5^ 
r= 3. 
5. 25. 125. 625. 
Powers of 5 mod 1000000 — 2*^ . 5^. 
therefore 
' and 
therefore 
5 has exp 2'^ = 16 mod 2^, 
t = 16, 
5® is divisible by 5®, 
r = 6. 
5. 25. 125. 625. 3125. 
15625’' 
78125 
390625 
953125 
765625 
828125 
140625 
703125 
515625 
578125 
S90625 
453125 
265625 
328125 
640625 
203125 
15625 
