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86 is carréphobic - approach of √86 ~ 9.2736184955

Subsequent approximations of √86 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 6 7 8 9 19 28 37 65 102 575 677 779 881 983 1864 2847 7558 10405 96492 106897 117302 127707 138112 148517 158922 169327 179732 190137 390679 580816 770953 1351769 2122722 11965379 14088101 16210823 18333545 20456267 38789812 59246079 157281970 216528049 2007998520 ... 0 1 1 1 1 1 1 1 1 1 1 2 3 4 7 11 62 73 84 95 106 201 307 815 1122 10405 11527 12649 13771 14893 16015 17137 18259 19381 20503 42128 62631 83134 145765 228899 1290260 1519159 1748058 1976957 2205856 4182813 6388669 16960151 23348820 216528049 ...

 Diophantine equation: s2-86p2 = 1 d = distance to nearest square N2: +5 Smallest non-trivial s: (2*81+5)/5 rational: 167/5 actual: 10405 ⇒ F=20810 Smallest non-trivial p: 2*9/5 rational: 18/5 actual: 1122 ⇒ primus foldage=1122 v-value qt-blocks: 1022-86*112: -2 Number of series: 24

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 10405 216528049 ... p 0 1122 23348820 ...

 In the numerator: U(1,10405)20810 = 1/2*U(2,20810)20810 - half the secundus of 20810. In the denominator: U(0,1122)20810 = 1122*U(0,1)20810 - the 1122-fold primus of 20810. as well as ... In the numerator: U(0,96492)20810 = 96492*U(0,1)20810 - the 86*1122-fold primus of 20810. In the denominator: U(1,10405)20810 = 1/2*U(2,20810)20810 - half the secundus of 20810. and ... In the numerator: U(-102,102)20810 = 102*U(-1,1)20810 - the 102-fold quartus of 20810. In the denominator: U(11,11)20810 = 11*U(1,1)20810 - the 11-fold tertius of 20810.