Solutions of Pell equation x2 - ny2 = ±1,
| n | integer part | length of fraction part | fraction part | Pell x | Pell y | x2-ny2 |
|---|---|---|---|---|---|---|
| 2 | 1 | 1 | 2 | 1 | 1 | -1 |
| 3 | 1 | 2 | 1, 2 | 2 | 1 | 1 |
| 5 | 2 | 1 | 4 | 2 | 1 | -1 |
| 6 | 2 | 2 | 2, 4 | 5 | 2 | 1 |
| 7 | 2 | 4 | 1, 1, 1, 4 | 8 | 3 | 1 |
| 10 | 3 | 1 | 6 | 3 | 1 | -1 |
| 11 | 3 | 2 | 3, 6 | 10 | 3 | 1 |
| 13 | 3 | 5 | 1, 1, 1, 1, 6 | 18 | 5 | -1 |
| 14 | 3 | 4 | 1, 2, 1, 6 | 15 | 4 | 1 |
| 15 | 3 | 2 | 1, 6 | 4 | 1 | 1 |
| 17 | 4 | 1 | 8 | 4 | 1 | -1 |
| 19 | 4 | 6 | 2, 1, 3, 1, 2, 8 | 170 | 39 | 1 |
| 21 | 4 | 6 | 1, 1, 2, 1, 1, 8 | 55 | 12 | 1 |
| 22 | 4 | 6 | 1, 2, 4, 2, 1, 8 | 197 | 42 | 1 |
| 23 | 4 | 4 | 1, 3, 1, 8 | 24 | 5 | 1 |
| 26 | 5 | 1 | 10 | 5 | 1 | -1 |
| 29 | 5 | 5 | 2, 1, 1, 2, 10 | 70 | 13 | -1 |
| 30 | 5 | 2 | 2, 10 | 11 | 2 | 1 |
| 31 | 5 | 8 | 1, 1, 3, 5, 3, 1, 1, 10 | 1520 | 273 | 1 |
| 33 | 5 | 4 | 1, 2, 1, 10 | 23 | 4 | 1 |
| 34 | 5 | 4 | 1, 4, 1, 10 | 35 | 6 | 1 |
| 35 | 5 | 2 | 1, 10 | 6 | 1 | 1 |
| 37 | 6 | 1 | 12 | 6 | 1 | -1 |
| 38 | 6 | 2 | 6, 12 | 37 | 6 | 1 |
| 39 | 6 | 2 | 4, 12 | 25 | 4 | 1 |
| 41 | 6 | 3 | 2, 2, 12 | 32 | 5 | -1 |
| 42 | 6 | 2 | 2, 12 | 13 | 2 | 1 |
| 43 | 6 | 10 | 1, 1, 3, 1, 5, 1, 3, 1, 1, 12 | 3482 | 531 | 1 |
| 46 | 6 | 12 | 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12 | 24335 | 3588 | 1 |
| 47 | 6 | 4 | 1, 5, 1, 12 | 48 | 7 | 1 |
| 51 | 7 | 2 | 7, 14 | 50 | 7 | 1 |
| 53 | 7 | 5 | 3, 1, 1, 3, 14 | 182 | 25 | -1 |
| 55 | 7 | 4 | 2, 2, 2, 14 | 89 | 12 | 1 |
| 57 | 7 | 6 | 1, 1, 4, 1, 1, 14 | 151 | 20 | 1 |
| 58 | 7 | 7 | 1, 1, 1, 1, 1, 1, 14 | 99 | 13 | -1 |
| 59 | 7 | 6 | 1, 2, 7, 2, 1, 14 | 530 | 69 | 1 |
| 61 | 7 | 11 | 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14 | 29718 | 3805 | -1 |
| 62 | 7 | 4 | 1, 6, 1, 14 | 63 | 8 | 1 |
| 65 | 8 | 1 | 16 | 8 | 1 | -1 |
| 66 | 8 | 2 | 8, 16 | 65 | 8 | 1 |
| 67 | 8 | 10 | 5, 2, 1, 1, 7, 1, 1, 2, 5, 16 | 48842 | 5967 | 1 |
| 69 | 8 | 8 | 3, 3, 1, 4, 1, 3, 3, 16 | 7775 | 936 | 1 |
| 70 | 8 | 6 | 2, 1, 2, 1, 2, 16 | 251 | 30 | 1 |
| 71 | 8 | 8 | 2, 2, 1, 7, 1, 2, 2, 16 | 3480 | 413 | 1 |
| 73 | 8 | 7 | 1, 1, 5, 5, 1, 1, 16 | 1068 | 125 | -1 |
| 74 | 8 | 5 | 1, 1, 1, 1, 16 | 43 | 5 | -1 |
| 77 | 8 | 6 | 1, 3, 2, 3, 1, 16 | 351 | 40 | 1 |
| 78 | 8 | 4 | 1, 4, 1, 16 | 53 | 6 | 1 |
| 79 | 8 | 4 | 1, 7, 1, 16 | 80 | 9 | 1 |
| 82 | 9 | 1 | 18 | 9 | 1 | -1 |
| 83 | 9 | 2 | 9, 18 | 82 | 9 | 1 |
| 85 | 9 | 5 | 4, 1, 1, 4, 18 | 378 | 41 | -1 |
| 86 | 9 | 10 | 3, 1, 1, 1, 8, 1, 1, 1, 3, 18 | 10405 | 1122 | 1 |
| 87 | 9 | 2 | 3, 18 | 28 | 3 | 1 |
| 89 | 9 | 5 | 2, 3, 3, 2, 18 | 500 | 53 | -1 |
| 91 | 9 | 8 | 1, 1, 5, 1, 5, 1, 1, 18 | 1574 | 165 | 1 |
| 93 | 9 | 10 | 1, 1, 1, 4, 6, 4, 1, 1, 1, 18 | 12151 | 1260 | 1 |
| 94 | 9 | 16 | 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18 | 2143295 | 221064 | 1 |
| 95 | 9 | 4 | 1, 2, 1, 18 | 39 | 4 | 1 |
| 97 | 9 | 11 | 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18 | 5604 | 569 | -1 |
the pattern of fraction part of continued fraction of sqrt(n) is always palindromic as
a1, a2, ...... , ai, ...... , a2, a1, b
last "b" is twice of integer part
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