73 is carréphobic - approach of √73 ~ 8.5440037453
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 √73.
| Diophantine equation: | s2-73p2 = 1 | | | |
| d = distance to nearest square N2: | -8 | | | |
| Smallest non-trivial s: | (2*81-8)/8 | rational: 154/8 | actual: 2281249 | ⇒ F=4562498 |
| Smallest non-trivial p: | 2*9/8 | rational: 18/8 | actual: 267000 | ⇒ primus foldage=267000 |
| v-value qt-blocks: | 10682-73*1252: | -1 | | |
| Number of series: | 37 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 2281249 | 10408194000001 | ... |
| p | 0 | 267000 | 1218186966000 | ... |
| In the numerator: | U(1,2281249)4562498 | = | 1/2*U(2,4562498)4562498 | - | half the secundus of 4562498. |
| In the denominator: | U(0,267000)4562498 | = | 267000*U(0,1)4562498 | - | the 267000-fold primus of 4562498. |
| as well as ... |
| In the numerator: | U(0,19491000)4562498 | = | 19491000*U(0,1)4562498 | - | the 73*267000-fold primus of 4562498. |
| In the denominator: | U(1,2281249)4562498 | = | 1/2*U(2,4562498)4562498 | - | half the secundus of 4562498. |
| and ... |
| In the numerator: | U(-1068,1068)4562498 | = | 1068*U(-1,1)4562498 | - | the 1068-fold quartus of 4562498. |
| In the denominator: | U(125,125)4562498 | = | 125*U(1,1)4562498 | - | the 125-fold tertius of 4562498. |
