5 is carréphylic - approach of √5 ~ 2.2360679775
Subsequent approximations of √5 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-5p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*4+1)/1 | rational: 9 | actual: 9 | ⇒ F=18 |
| Smallest non-trivial p: | 2*2/1 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value qt-blocks: | 22-5*12: | -1 | | |
| Number of series: | 5 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 9 | 161 | 2889 | 51841 | 930249 | 16692641 | ... |
| p | 0 | 4 | 72 | 1292 | 23184 | 416020 | 7465176 | ... |
| In the numerator: | U(1,9)18 | = | 1/2*U(2,18)18 | - | half the secundus of 18. |
| In the denominator: | U(0,4)18 | = | 4*U(0,1)18 | - | the 4-fold primus of 18. |
| as well as ... |
| In the numerator: | U(0,20)18 | = | 20*U(0,1)18 | - | the 5*4-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(-2,2)18 | = | 2*U(-1,1)18 | - | the 2-fold quartus of 18. |
| In the denominator: | U(1,1)18 | = | | - | the tertius of 18. |
