Elements of Algebra

360 ELEMENTS PART II. TABLE, shewing for each value of $a$ the least numbers $m$ and $n$, that will give $m^2 = an^2 + 1$*; or that will render $an^2 + 1$ a square. $a$ $n$ $m$ $a$ $n$ $m$ 2 2 3 53 9100 66249 3 1 2 54 66 485 5 4 9 55 12 89 6 2 5 56 2 15 7 3 8 57 20 151 8 1 3 58 2574 19603 10 6 19 59 69 530 11 3 10 60 4 31 12 2 7 61 226153980 1766319049 13 180 649 62 8 63 14 4 15 63 1 8 15 1 4 17 8 33 65 16 129 18 4 17 66 8 65 19 39 170 67 5967 48842 20 2 9 68 4 33 21 12 55 69 936 7775 22 42 197 70 30 251 23 5 24 71 413 3480 24 1 5 72 2 17 26 10 51 73 267000 2281249 27 5 26 74 430 3699 28 24 127 75 3 26 29 1820 9801 76 6630 57799 30 2 11 77 40 351 31 273 1520 78 6 53 32 3 17 79 9 80 33 4 23 80 1 9 34 6 35 35 1 6 82 18 163 37 12 73 83 9 82 38 6 37 84 6 55 39 4 25 85 30996 285769 40 3 19 86 1122 10405 41 320 2049 87 3 28 42 2 13 88 21 197 43 531 3482 89 53000 500001 44 30 199 90 2 19 45 24 161 91 165 1574 46 3588 24335 92 120 1151 47 7 48 93 1260 12151 48 1 7 94 221064 2143295 50 14 99 95 4 39 51 7 50 96 5 49 52 90 649 97 6377352 62809633 98 10 99 99 1 10 * See Article 8 of the Additions by De la Grange.