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.
| 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. |
