David Speyer'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 = 4x^2+6x+2, P = 4x+3, Q = 2
n =    3: D = x^2+4x+3, P = x+2, Q = 1
n =    4: perfect square
n =    5: D = 16x^2+18x+5, P = 16x+9, Q = 4
n =    6: D = 4x^2+10x+6, P = 4x+5, Q = 2
n =    7: D = 9x^2+16x+7, P = 9x+8, Q = 3
n =    8: D = x^2+6x+8, P = x+3, Q = 1
n =    9: perfect square
n =   10: D = 36x^2+38x+10, P = 36x+19, Q = 6
n =   11: D = 9x^2+20x+11, P = 9x+10, Q = 3
n =   12: D = 4x^2+14x+12, P = 4x+7, Q = 2
n =   13: D = 32400x^2+1298x+13, P = 32400x+649, Q = 180
n =   14: D = 16x^2+30x+14, P = 16x+15, Q = 4
n =   15: D = x^2+8x+15, P = x+4, Q = 1
n =   16: perfect square
n =   17: D = 64x^2+66x+17, P = 64x+33, Q = 8
n =   18: D = 16x^2+34x+18, P = 16x+17, Q = 4
n =   19: D = 1521x^2+340x+19, P = 1521x+170, Q = 39
n =   20: D = 4x^2+18x+20, P = 4x+9, Q = 2
n =   21: D = 144x^2+110x+21, P = 144x+55, Q = 12
n =   22: D = 1764x^2+394x+22, P = 1764x+197, Q = 42
n =   23: D = 25x^2+48x+23, P = 25x+24, Q = 5
n =   24: D = x^2+10x+24, P = x+5, Q = 1
n =   25: perfect square
n =   26: D = 100x^2+102x+26, P = 100x+51, Q = 10
n =   27: D = 25x^2+52x+27, P = 25x+26, Q = 5
n =   28: D = 576x^2+254x+28, P = 576x+127, Q = 24
n =   29: D = 3312400x^2+19602x+29, P = 3312400x+9801, Q = 1820
n =   30: D = 4x^2+22x+30, P = 4x+11, Q = 2
n =   31: D = 74529x^2+3040x+31, P = 74529x+1520, Q = 273
n =   32: D = 9x^2+34x+32, P = 9x+17, Q = 3
n =   33: D = 16x^2+46x+33, P = 16x+23, Q = 4
n =   34: D = 36x^2+70x+34, P = 36x+35, Q = 6
n =   35: D = x^2+12x+35, P = x+6, Q = 1
n =   36: perfect square
n =   37: D = 144x^2+146x+37, P = 144x+73, Q = 12
n =   38: D = 36x^2+74x+38, P = 36x+37, Q = 6
n =   39: D = 16x^2+50x+39, P = 16x+25, Q = 4
n =   40: D = 9x^2+38x+40, P = 9x+19, Q = 3
n =   41: D = 102400x^2+4098x+41, P = 102400x+2049, Q = 320
n =   42: D = 4x^2+26x+42, P = 4x+13, Q = 2
n =   43: D = 281961x^2+6964x+43, P = 281961x+3482, Q = 531
n =   44: D = 900x^2+398x+44, P = 900x+199, Q = 30
n =   45: D = 576x^2+322x+45, P = 576x+161, Q = 24
n =   46: D = 12873744x^2+48670x+46, P = 12873744x+24335, Q = 3588
n =   47: D = 49x^2+96x+47, P = 49x+48, Q = 7
n =   48: D = x^2+14x+48, P = x+7, Q = 1
n =   49: perfect square
n =   50: D = 196x^2+198x+50, P = 196x+99, Q = 14
n =   51: D = 49x^2+100x+51, P = 49x+50, Q = 7
n =   52: D = 8100x^2+1298x+52, P = 8100x+649, Q = 90
n =   53: D = 82810000x^2+132498x+53, P = 82810000x+66249, Q = 9100
n =   54: D = 4356x^2+970x+54, P = 4356x+485, Q = 66
n =   55: D = 144x^2+178x+55, P = 144x+89, Q = 12
n =   56: D = 4x^2+30x+56, P = 4x+15, Q = 2
n =   57: D = 400x^2+302x+57, P = 400x+151, Q = 20
n =   58: D = 6625476x^2+39206x+58, P = 6625476x+19603, Q = 2574
n =   59: D = 4761x^2+1060x+59, P = 4761x+530, Q = 69
n =   60: D = 16x^2+62x+60, P = 16x+31, Q = 4
n =   61: D = 51145622669840400x^2+3532638098x+61, P = 51145622669840400x+1766319049, Q = 226153980
n =   62: D = 64x^2+126x+62, P = 64x+63, Q = 8
n =   63: D = x^2+16x+63, P = x+8, Q = 1
n =   64: perfect square
n =   65: D = 256x^2+258x+65, P = 256x+129, Q = 16
n =   66: D = 64x^2+130x+66, P = 64x+65, Q = 8
n =   67: D = 35605089x^2+97684x+67, P = 35605089x+48842, Q = 5967
n =   68: D = 16x^2+66x+68, P = 16x+33, Q = 4
n =   69: D = 876096x^2+15550x+69, P = 876096x+7775, Q = 936
n =   70: D = 900x^2+502x+70, P = 900x+251, Q = 30
n =   71: D = 170569x^2+6960x+71, P = 170569x+3480, Q = 413
n =   72: D = 4x^2+34x+72, P = 4x+17, Q = 2
n =   73: D = 71289000000x^2+4562498x+73, P = 71289000000x+2281249, Q = 267000
n =   74: D = 184900x^2+7398x+74, P = 184900x+3699, Q = 430
n =   75: D = 9x^2+52x+75, P = 9x+26, Q = 3
n =   76: D = 43956900x^2+115598x+76, P = 43956900x+57799, Q = 6630
n =   77: D = 1600x^2+702x+77, P = 1600x+351, Q = 40
n =   78: D = 36x^2+106x+78, P = 36x+53, Q = 6
n =   79: D = 81x^2+160x+79, P = 81x+80, Q = 9
n =   80: D = x^2+18x+80, P = x+9, Q = 1
n =   81: perfect square
n =   82: D = 324x^2+326x+82, P = 324x+163, Q = 18
n =   83: D = 81x^2+164x+83, P = 81x+82, Q = 9
n =   84: D = 36x^2+110x+84, P = 36x+55, Q = 6
n =   85: D = 960752016x^2+571538x+85, P = 960752016x+285769, Q = 30996
n =   86: D = 1258884x^2+20810x+86, P = 1258884x+10405, Q = 1122
n =   87: D = 9x^2+56x+87, P = 9x+28, Q = 3
n =   88: D = 441x^2+394x+88, P = 441x+197, Q = 21
n =   89: D = 2809000000x^2+1000002x+89, P = 2809000000x+500001, Q = 53000
n =   90: D = 4x^2+38x+90, P = 4x+19, Q = 2
n =   91: D = 27225x^2+3148x+91, P = 27225x+1574, Q = 165
n =   92: D = 14400x^2+2302x+92, P = 14400x+1151, Q = 120
n =   93: D = 1587600x^2+24302x+93, P = 1587600x+12151, Q = 1260
n =   94: D = 48869292096x^2+4286590x+94, P = 48869292096x+2143295, Q = 221064
n =   95: D = 16x^2+78x+95, P = 16x+39, Q = 4
n =   96: D = 25x^2+98x+96, P = 25x+49, Q = 5
n =   97: D = 40670618531904x^2+125619266x+97, P = 40670618531904x+62809633, Q = 6377352
n =   98: D = 100x^2+198x+98, P = 100x+99, Q = 10
n =   99: D = x^2+20x+99, P = x+10, Q = 1
n =  100: perfect square