99 is carréphylic - approach of √99=3√11 ~ 9.9498743711
Subsequent approximations of √99 - the position of a fraction indicates whether it is over or under the root-value.
99 is one less than a square, so the exception mentioned in
on root approach applies: 199 and 20, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being
10 and
1 because
102-99*12 = 1 satisfies the diophantine equation.
| Diophantine equation: | s2-99p2 = 1 | | | |
| d = distance to nearest square N2: | -1 | | | |
| Smallest non-trivial s: | (2*100-1)/1 | rational: 199 | actual: 199 (10) | ⇒ F=398 (20) |
| Smallest non-trivial p: | 2*10/1 | rational: 20 | actual: 20 (1) | ⇒ primus foldage=20 (1) |
| v-value tq-blocks: | 92-99*12: | -18 | | |
| Number of series: | 11 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 10 | 199 | 3970 | ... |
| p | 0 | 1 | 20 | 399 | ... |
| In the numerator: | U(1,10)20 | = | 1/2*U(2,20)20 | - | half the secundus of 20. |
| In the denominator: | U(0,1)20 | = | | - | the primus of 20. |
| as well as ... |
| In the numerator: | U(0,99)20 | = | 99*U(0,1)20 | - | the 99-fold primus of 20. |
| In the denominator: | U(1,10)20 | = | 1/2*U(2,20)20 | - | half the secundus of 20. |
| and ... |
| In the numerator: | U(-9,9)20 | = | 9*U(-1,1)20 | - | the 9-fold quartus of 20. |
| In the denominator: | U(1,1)20 | = | | - | the tertius of 20. |
