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Smallest solutions (with y > 0) of x2ny2 = 1 for n ≤ 100: (no solution other than (x,y) = (1,0) if n is square, and there are infinitely many solutions for all nonsquare n)

n x y n x y n x y n x y
1 1 0 31 61 10 61 920201 10X620 91 1588E1X4279461 1846395623990
2 3 2 32 31 6 62 2183 2EX 92 19 2
3 2 1 33 21 4 63 22 3 93 207 24
4 1 0 34 17 3 64 29547 3X06 94 X7 10
5 9 4 35 1229 228 65 253 34 95 4X0E69 55694
6 5 2 36 11 2 66 45 6 96 715 80
7 8 3 37 2022 383 67 68 9 97 79X 89
8 3 1 38 147 26 68 9 1 98 5809 63X
9 1 0 39 115 20 69 1 0 99 461 50
X 17 6 3X 120EE 20E0 6X 117 16 9X 129745 14426
E X 3 3E 40 7 6E 6X 9 9E X0 E
10 7 2 40 7 1 70 47 6 X0 E 1
11 461 130 41 1 0 71 119461 15E30 X1 1 0
12 13 4 42 83 12 72 6031 796 X2 183 1X
13 4 1 43 42 7 73 24 3 X3 X2 E
14 1 0 44 461 76 74 145 19 X4 166X0X7 180180
15 29 8 45 32409 5324 75 201429 26808 X5 38X409 40198
16 15 4 46 345 56 76 17 2 X6 315 34
17 122 33 47 75 10 77 XE2 119 X7 1701768 182E13
18 9 2 48 13 2 78 7EE X0 X8 401 43
19 47 10 49 107 18 79 7047 890 X9 9907 X38
1X 145 36 4X E417 15X6 7X 8743EE X7E20 XX 3917 3E6
1E 20 5 4E 382 59 7E 33 4 XE 6182 653
20 5 1 50 27 4 80 41 5 E0 1E 2
21 1 0 51 413653461 638X4190 81 19050201 2176720 E1 X4X047 X9X90
22 43 X 52 53 8 82 83 X E2 70545 7366
23 22 5 53 8 1 83 X 1 E3 184 19
24 X7 20 54 1 0 84 1 0 E4 2E 3
25 5809 1078 55 X9 14 85 149 18 E5 2054369 210914
26 E 2 56 55 8 86 85 X E6 3E 4
27 X68 1X9 57 24322 3553 87 XE808 10E83 E7 21E86182 2253239
28 15 3 58 29 4 88 43 5 E8 5E 6
29 1E 4 59 45EE 660 89 35 4 E9 7E 8
2X 2E 6 5X 18E 26 8X X8E0X17 1063216 EX EE 10
2E 6 1 5E 2020 2X5 8E 682 79 EE 10 1
30 1 0 60 15 2 90 947 XX 100 1 0

Smallest solutions of x2ny2 = −1 for n ≤ 410: (if solvable, all solvable n end with 1, 2, 5 or X (the only single-digit solvable n), but the converse is not true, e.g. this equation is not solvable for n = 12 and n = 1X)

n x y n x y n x y n x y
1 0 1 95 548 61 1XX 993 71 2E1 2X377X1053E07976 1808E170959EX55
2 1 1 X2 E 1 1E1 188E551246 12E5E96E5 2E5 1X4 11
5 2 1 X5 48X 51 1E5 433578 30871 301 149964X150 98455E01
X 3 1 XX 49 5 202 15 1 30X 19 1
11 16 5 E5 1014 105 205 152X 101 311 2846 165
15 4 1 101 10 1 20X 179019 11891 315 53553918 2EE2721
22 5 1 105 55892 5475 221 3659E880 2499851 321 E551131X00 651841585
25 5X 11 111 1750446 167211 222 30E 21 322 8E 5
31 6 1 122 11 1 225 15008X E565 325 81867EX 467405
35 28 5 125 792 71 231 16 1 341 3X5E50 21535
42 7 1 131 270192576 237E3075 241 244247060 16646E35 345 1X 1
45 132 21 135 58 5 242 17E 11 351 28E9X6 159E1
4X 83 11 141 710XE0 615X1 24X 79 5 365 E0641292 5X5X7X5
51 15246 2251 145 12 1 251 53E6 351 375 36EE0474 1X72985
55 8 1 14X 1999 165 255 352X8 2241 382 1E 1
61 750 X5 162 18E 15 262 17 1 385 365X 1X1
62 37 5 16X 13 1 265 2002 131 38X 33E63 1881
6X 9 1 171 EX6 95 26X 233 15 391 74453147696X59X76 397127780X3X01X5
71 276 35 175 11498 X65 271 2E66 1X1 3X2 84X45 4351
75 358 45 181 1E946450 1647155 285 8XX 55 3X5 9X 5
81 32E0 3E5 18X 26X3 1E5 28X E0361363 67E8925 3E1 4E35246 25E1E5
85 X 1 195 14 1 291 3E76185946 24824X131 3E5 689598508 34786XX5
8X 2399 285 1X1 3620 271 295 18 1 401 20 1
91 2E88946 350945 1X5 6X 5 2X1 19836472520 10X5474665 40X 96X173E03 48E1E475
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