5 is carréphylic - approach of √35 ~ 5.9160797831
Subsequent approximations of √35 - the position of a fraction indicates whether it is over or under the root-value.
35 is one less than a square, so the exception mentioned in
on root approach applies: 71 and 12, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being
6 and
1 because
62-35*12 = 1 satisfies the diophantine equation.
| Diophantine equation: | s2-35p2 = 1 | | | |
| d = distance to nearest square N2: | -1 | | | |
| Smallest non-trivial s: | (2*36-1)/1 | rational: 71 | actual: 71 (6) | ⇒ F=142 (12) |
| Smallest non-trivial p: | 2*6/1 | rational: 12 | actual: 12 (1) | ⇒ primus foldage=12 (1) |
| v-value qt-blocks: | 52-35*12: | -10 | | |
| Number of series: | 7 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 6 | 71 | 846 | 10081 | 120126 | 1431431 | 17057046 | ... |
| p | 0 | 1 | 12 | 143 | 1704 | 20305 | 241956 | 2883167 | ... |
| In the numerator: | U(1,6)12 | = | 1/2*U(2,12)12 | - | half the secundus of 12. |
| In the denominator: | U(0,1)12 | = | | - | the primus of 12. |
| as well as ... |
| In the numerator: | U(0,35)12 | = | 35*U(0,1)12 | - | the 35-fold primus of 12. |
| In the denominator: | U(1,6)12 | = | 1/2*U(2,12)12 | - | half the secundus of 12. |
| and ... |
| In the numerator: | U(-5,5)12 | = | 5*U(-1,1)12 | - | the 5-fold quartus of 12. |
| In the denominator: | U(1,1)12 | = | | - | the tertius of 12. |
