93 is carréphobic - approach of √93 ~ 9.6436507610
Subsequent approximations of √93 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-93p2 = 1 | | | |
| d = distance to nearest square N2: | -7 | | | |
| Smallest non-trivial s: | (2*100-7)/7 | rational: 193/7 | actual: 12151 | ⇒ F=24302 |
| Smallest non-trivial p: | 2*10/7 | rational: 20/7 | actual: 1260 | ⇒ primus foldage=1260 |
| v-value qt-blocks: | 1352-93*142: | -3 | | |
| Number of series: | 24 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 12151 | 295293601 | ... |
| p | 0 | 1260 | 30620520 | ... |
| In the numerator: | U(1,12151)24302 | = | 1/2*U(2,24302)24302 | - | half the secundus of 24302. |
| In the denominator: | U(0,1260)24302 | = | 1260*U(0,1)24302 | - | the 1260-fold primus of 24302. |
| as well as ... |
| In the numerator: | U(0,117180)24302 | = | 117180*U(0,1)24302 | - | the 93*1260-fold primus of 24302. |
| In the denominator: | U(1,12151)24302 | = | 1/2*U(2,24302)24302 | - | half the secundus of 24302. |
| and ... |
| In the numerator: | U(-135,135)24302 | = | 135*U(-1,1)24302 | - | the 135-fold quartus of 24302. |
| In the denominator: | U(14,14)24302 | = | 14*U(1,1)24302 | - | the 14-fold tertius of 24302. |
