17 is carréphylic - approach of √17 ~ 4.1231056256
Subsequent approximations of √17 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-17p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*16+1)/1 | rational: 33 | actual: 33 | ⇒ F=38 |
| Smallest non-trivial p: | 2*4/1 | rational: 8 | actual: 8 | ⇒ primus foldage=8 |
| v-value qt-blocks: | 42-17*12: | -1 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 33 | 2177 | 143649 | 9478657 | ... |
| p | 0 | 8 | 528 | 34840 | 2298912 | ... |
| In the numerator: | U(1,33)66 | = | 1/2*U(2,66)66 | - | half the secundus of 66. |
| In the denominator: | U(0,8)66 | = | 8*U(0,1)66 | - | the 8-fold primus of 66. |
| as well as ... |
| In the numerator: | U(0,136)66 | = | 136*U(0,1)66 | - | the 17*8-fold primus of 66. |
| In the denominator: | U(1,33)66 | = | 1/2*U(2,66)66 | - | half the secundus of 66. |
| and ... |
| In the numerator: | U(-4,4)66 | = | 4*U(-1,1)66 | - | the 4-fold quartus of 66. |
| In the denominator: | U(1,1)66 | = | | - | the tertius of 66. |
