85 is carréphobic - approach of √85 ~ 9.2195444573
Using the
incremental profile, the questionmarks can be filled in - the position of a fraction indicates whether it is over or under the root-value. The positioning of the missing fractions corresponds to the first section.
Subsequent approximations of √85.
| Diophantine equation: | s2-85p2 = 1 | | | |
| d = distance to nearest square N2: | +4 | | | |
| Smallest non-trivial s: | (2*81+4)/4 | rational: 166/4 | actual: 285769 | ⇒ F=571538 |
| Smallest non-trivial p: | 2*9/4 | rational: 18/4 | actual: 30996 | ⇒ primus foldage=30996 |
| v-value qt-blocks: | 3782-85*412: | -1 | | |
| Number of series: | 33 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 285769 | 163327842721 | ... |
| p | 0 | 30996 | 17715391848 | ... |
| In the numerator: | U(1,285769)571538 | = | 1/2*U(2,571538)571538 | - | half the secundus of 571538. |
| In the denominator: | U(0,30996)571538 | = | 30996*U(0,1)571538 | - | the 30996-fold primus of 571538. |
| as well as ... |
| In the numerator: | U(0,2634660)571538 | = | 2634660*U(0,1)571538 | - | the 85*30996-fold primus of 571538. |
| In the denominator: | U(1,285769)571538 | = | 1/2*U(2,571538)571538 | - | half the secundus of 571538. |
| and ... |
| In the numerator: | U(-378,378)571538 | = | 378*U(-1,1)571538 | - | the 378-fold quartus of 571538. |
| In the denominator: | U(41,41)571538 | = | 41*U(1,1)571538 | - | the 41-fold tertius of 571538. |
