20 is carréphylic - approach of √20=2√5 ~ 4.4721359550
Subsequent approximations of √20 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-20p2 = 1 | | | |
| d = distance to nearest square N2: | +4 | | | |
| Smallest non-trivial s: | (2*16+4)/4 | rational: 9 | actual: 9 | ⇒ F=18 |
| Smallest non-trivial p: | 2*4/4 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 42-20*12: | -4 | | |
| Number of series: | 6 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 9 | 161 | 2889 | 51841 | 51841 | 16692641 | 299537289 | 5374978561 | ... |
| p | 0 | 2 | 36 | 646 | 11592 | 51841 | 3732588 | 66978574 | 1201881744 | ... |
| In the numerator: | U(1,9)18 | = | 1/2*U(2,18)18 | - | half the secundus of 18. |
| In the denominator: | U(0,2)18 | = | 2*U(0,1)18 | - | the 2-fold primus of 18. |
| as well as ... |
| In the numerator: | U(0,40)18 | = | 40*U(0,1)18 | - | the 20*2-fold primus of 18. |
| In the denominator: | U(1,9)18 | = | 1/2*U(2,18)18 | - | half the secundus of 18. |
| and ... |
| In the numerator: | U(-4,4)18 | = | 4*U(-1,1)18 | - | the 4-fold quartus of 18. |
| In the denominator: | U(1,1)18 | = | | - | the tertius of 18. |
