18.5 The period length of a prime 529
Project
It is known that the number
N= 19000458461599776807277716631is a perfect cube. Find its cube rootM. Verify thatN=N 0 the twenty-
eight numbersNi, 1 ≤i≤ 28 which are formed by cyclic permutations
of its digits are all divisible by the cube root ofN.
i Ni Ni÷M
0 19000458461599776807277716631
1 90004584615997768072777166311
2 45846159977680727771663119
3 458461599776807277716631190
4 4584615997768072777166311900
5 45846159977680727771663119000
6 58461599776807277716631190004
7 84615997768072777166311900045
8 46159977680727771663119000458
9 61599776807277716631190004584
10 15997768072777166311900045846
11 59977680727771663119000458461
12 99776807277716631190004584615
13 97768072777166311900045846159
14 77680727771663119000458461599
15 76807277716631190004584615997
16 68072777166311900045846159977
17 80727771663119000458461599776
18 7277716631190004584615997768
19 72777166311900045846159977680
20 27771663119000458461599776807
21 77716631190004584615997768072
22 77166311900045846159977680727
23 71663119000458461599776807277
24 16631190004584615997768072777
25 66311900045846159977680727771
26 63119000458461599776807277716
27 31190004584615997768072777166
28 11900045846159977680727771663