Leonardo's solution to Pell's equation P^2-DQ^2 = 1 in polynomials, where D(0) = n; tabulated for n <= 100
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n =   1: perfect square
n =   2: D = 64x^2+32x+2, P = 64x^2+32x+3, Q = 8x+2
n =   3: D = 9x^2+18x+3, P = 3x^2+6x+2, Q = x+1
n =   4: perfect square
n =   5: D = 1600x^2+200x+5, P = 2560x^2+320x+9, Q = 64x+4
n =   6: D = 144x^2+72x+6, P = 96x^2+48x+5, Q = 8x+2
n =   7: D = 729x^2+162x+7, P = 729x^2+162x+8, Q = 27x+3
n =   8: D = 16x^2+32x+8, P = 4x^2+8x+3, Q = x+1
n =   9: perfect square
n =  10: D = 14400x^2+800x+10, P = 25920x^2+1440x+19, Q = 216x+6
n =  11: D = 1089x^2+242x+11, P = 891x^2+198x+10, Q = 27x+3
n =  12: D = 256x^2+128x+12, P = 128x^2+64x+7, Q = 8x+2
n =  13: D = 13689000000x^2+845000x+13, P = 682344000000x^2+42120000x+649, Q = 5832000x+180
n =  14: D = 4096x^2+512x+14, P = 4096x^2+512x+15, Q = 64x+4
n =  15: D = 25x^2+50x+15, P = 5x^2+10x+4, Q = x+1
n =  16: perfect square
n =  17: D = 73984x^2+2312x+17, P = 139264x^2+4352x+33, Q = 512x+8
n =  18: D = 5184x^2+648x+18, P = 4608x^2+576x+17, Q = 64x+4
n =  19: D = 44475561x^2+58482x+19, P = 395598411x^2+520182x+170, Q = 59319x+39
n =  20: D = 400x^2+200x+20, P = 160x^2+80x+9, Q = 8x+2
n =  21: D = 451584x^2+6272x+21, P = 1161216x^2+16128x+55, Q = 1728x+12
n =  22: D = 69155856x^2+78408x+22, P = 616115808x^2+698544x+197, Q = 74088x+42
n =  23: D = 15625x^2+1250x+23, P = 15625x^2+1250x+24, Q = 125x+5
n =  24: D = 36x^2+72x+24, P = 6x^2+12x+5, Q = x+1
n =  25: perfect square
n =  26: D = 270400x^2+5408x+26, P = 520000x^2+10400x+51, Q = 1000x+10
n =  27: D = 18225x^2+1458x+27, P = 16875x^2+1350x+26, Q = 125x+5
n =  28: D = 9437184x^2+32768x+28, P = 42467328x^2+147456x+127, Q = 13824x+24
n =  29: D = 318252755329600x^2+192158408x+29, P = 107547482835520000x^2+64936289600x+9801, Q = 6028568000x+1820
n =  30: D = 576x^2+288x+30, P = 192x^2+96x+11, Q = 8x+2
n =  31: D = 172418444289x^2+4626882x+31, P = 8448503770161x^2+226717218x+1520, Q = 20346417x+273
n =  32: D = 2916x^2+648x+32, P = 1458x^2+324x+17, Q = 27x+3
n =  33: D = 9216x^2+1152x+33, P = 6144x^2+768x+23, Q = 64x+4
n =  34: D = 46656x^2+2592x+34, P = 46656x^2+2592x+35, Q = 216x+6
n =  35: D = 49x^2+98x+35, P = 7x^2+14x+6, Q = x+1
n =  36: perfect square
n =  37: D = 788544x^2+10952x+37, P = 1534464x^2+21312x+73, Q = 1728x+12
n =  38: D = 51984x^2+2888x+38, P = 49248x^2+2736x+37, Q = 216x+6
n =  39: D = 10816x^2+1352x+39, P = 6656x^2+832x+25, Q = 64x+4
n =  40: D = 3600x^2+800x+40, P = 1620x^2+360x+19, Q = 27x+3
n =  41: D = 430336000000x^2+8405000x+41, P = 21495808000000x^2+419840000x+2049, Q = 32768000x+320
n =  42: D = 784x^2+392x+42, P = 224x^2+112x+13, Q = 8x+2
n =  43: D = 3420550377729x^2+24262578x+43, P = 276905485229643x^2+1964140326x+3482, Q = 149721291x+531
n =  44: D = 36000000x^2+80000x+44, P = 162000000x^2+360000x+199, Q = 27000x+30
n =  45: D = 15116544x^2+52488x+45, P = 53747712x^2+186624x+161, Q = 13824x+24
n =  46: D = 7624357681434624x^2+1184481792x+46, P = 4033285213478916096x^2+626590867968x+24335, Q = 46190993472x+3588
n =  47: D = 117649x^2+4802x+47, P = 117649x^2+4802x+48, Q = 343x+7
n =  48: D = 64x^2+128x+48, P = 8x^2+16x+7, Q = x+1
n =  49: perfect square
n =  50: D = 1960000x^2+20000x+50, P = 3841600x^2+39200x+99, Q = 2744x+14
n =  51: D = 127449x^2+5202x+51, P = 122451x^2+4998x+50, Q = 343x+7
n =  52: D = 3422250000x^2+845000x+52, P = 42646500000x^2+10530000x+649, Q = 729000x+90
n =  53: D = 363458265625000000x^2+8778125000x+53, P = 454309116625000000000x^2+10972325000000x+66249, Q = 753571000000x+9100
n =  54: D = 1028869776x^2+472392x+54, P = 9221721696x^2+4234032x+485, Q = 287496x+66
n =  55: D = 1166400x^2+16200x+55, P = 1866240x^2+25920x+89, Q = 1728x+12
n =  56: D = 1024x^2+512x+56, P = 256x^2+128x+15, Q = 8x+2
n =  57: D = 9241600x^2+46208x+57, P = 24320000x^2+121600x+151, Q = 8000x+20
n =  58: D = 2546281840804416x^2+768633632x+58, P = 860555459369795904x^2+259771663008x+19603, Q = 17053975224x+2574
n =  59: D = 1342416321x^2+563922x+59, P = 12036241251x^2+5056182x+530, Q = 328509x+69
n =  60: D = 16384x^2+2048x+60, P = 8192x^2+1024x+31, Q = 64x+4
n =  61: D = 159568357996106202306471367761000000x^2+6239765972785805000x+61, P = 4620469347321401556801014926932252648000000x^2+180678975291701917959240000x+1766319049, Q = 11566786126362632424792000x+226153980
n =  62: D = 262144x^2+8192x+62, P = 262144x^2+8192x+63, Q = 512x+8
n =  63: D = 81x^2+162x+63, P = 9x^2+18x+8, Q = x+1
n =  64: perfect square
n =  65: D = 4326400x^2+33800x+65, P = 8519680x^2+66560x+129, Q = 4096x+16
n =  66: D = 278784x^2+8712x+66, P = 270336x^2+8448x+65, Q = 512x+8
n =  67: D = 84940876419484761x^2+4771277298x+67, P = 61919363361254555403x^2+3478118724054x+48842, Q = 212455566063x+5967
n =  68: D = 18496x^2+2312x+68, P = 8704x^2+1088x+33, Q = 64x+4
n =  69: D = 52974174928896x^2+120932352x+69, P = 5968423708655616x^2+13625044992x+7775, Q = 820025856x+936
n =  70: D = 57153600x^2+127008x+70, P = 204120000x^2+453600x+251, Q = 27000x+30
n =  71: D = 2066846148409x^2+24234722x+71, P = 101275461272041x^2+1187501378x+3480, Q = 70444997x+413
n =  72: D = 1296x^2+648x+72, P = 288x^2+144x+17, Q = 8x+2
n =  73: D = 370995196289062500000000x^2+10408203125000x+73, P = 11593589719781250000000000000x^2+325256062500000000x+2281249, Q = 19034163000000000x+267000
n =  74: D = 2531281000000x^2+27380000x+74, P = 126495637000000x^2+1368260000x+3699, Q = 79507000x+430
n =  75: D = 6561x^2+1458x+75, P = 2187x^2+486x+26, Q = 27x+3
n =  76: D = 146852969796000000x^2+6681680000x+76, P = 111681683529858000000x^2+5081417640000x+57799, Q = 291434247000x+6630
n =  77: D = 198246400x^2+247808x+77, P = 901120000x^2+1126400x+351, Q = 64000x+40
n =  78: D = 104976x^2+5832x+78, P = 69984x^2+3888x+53, Q = 216x+6
n =  79: D = 531441x^2+13122x+79, P = 531441x^2+13122x+80, Q = 729x+9
n =  80: D = 100x^2+200x+80, P = 10x^2+20x+9, Q = x+1
n =  81: perfect square
n =  82: D = 8714304x^2+53792x+82, P = 17216064x^2+106272x+163, Q = 5832x+18
n =  83: D = 558009x^2+13778x+83, P = 544563x^2+13446x+82, Q = 729x+9
n =  84: D = 112896x^2+6272x+84, P = 72576x^2+4032x+55, Q = 216x+6
n =  85: D = 78459326189292686400x^2+163328985800x+85, P = 263778408546609322437120x^2+549108207224640x+285769, Q = 29779469487936x+30996
n =  86: D = 136318047483024x^2+216569672x+86, P = 16491313558295136x^2+26199893808x+10405, Q = 1412467848x+1122
n =  87: D = 7569x^2+1682x+87, P = 2349x^2+522x+28, Q = 27x+3
n =  88: D = 17288964x^2+78408x+88, P = 38507238x^2+174636x+197, Q = 9261x+21
n =  89: D = 702255618011236000000x^2+500004000008x+89, P = 3945256280962000000000000x^2+2809011236000000x+500001, Q = 148877000000000x+53000
n =  90: D = 1600x^2+800x+90, P = 320x^2+160x+19, Q = 8x+2
n =  91: D = 67535015625x^2+4961250x+91, P = 1167390984375x^2+85758750x+1574, Q = 4492125x+165
n =  92: D = 19110297600x^2+2654208x+92, P = 238878720000x^2+33177600x+1151, Q = 1728000x+120
n =  93: D = 234442644710400x^2+295342208x+93, P = 30628797131520000x^2+38585030400x+12151, Q = 2000376000x+1260
n =  94: D = 224491734219348343259136x^2+9187435487232x+94, P = 5118636031935361574651559936x^2+209482716544376832x+2143295, Q = 10803241187910144x+221064
n =  95: D = 25600x^2+3200x+95, P = 10240x^2+1280x+39, Q = 64x+4
n =  96: D = 62500x^2+5000x+96, P = 31250x^2+2500x+49, Q = 125x+5
n =  97: D = 160447628650475677482804052224x^2+7890100246427912x+97, P = 103893366090814782759233080910290944x^2+5109013329085015126272x+62809633, Q = 259370850435675038208x+6377352
n =  98: D = 1000000x^2+20000x+98, P = 1000000x^2+20000x+99, Q = 1000x+10
n =  99: D = 121x^2+242x+99, P = 11x^2+22x+10, Q = x+1
n = 100: perfect square