23 is carréphylic - approach of √23 ~ 4.7958315233
Subsequent approximations of √23 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-23p2 = 1 | | | |
| d = distance to nearest square N2: | -2 | | | |
| Smallest non-trivial s: | (2*25-2)/2 | rational: 24 | actual: 24 | ⇒ F=48 |
| Smallest non-trivial p: | 2*5/2 | rational: 5 | actual: 5 | ⇒ primus foldage=5 |
| v-value tq-blocks: | 52-23*12: | +2 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 24 | 1151 | 55224 | 2649601 | 127125624 | ... |
| p | 0 | 5 | 240 | 11515 | 552480 | 26507525 | ... |
| In the numerator: | U(1,24)48 | = | 1/2*U(2,48)48 | - | half the secundus of 48. |
| In the denominator: | U(0,5)48 | = | 5*U(0,1)48 | - | the 5-fold primus of 48. |
| as well as ... |
| In the numerator: | U(0,115)48 | = | 115*U(0,1)48 | - | the 23*5-fold primus of 48. |
| In the denominator: | U(1,24)48 | = | 1/2*U(2,48)48 | - | half the secundus of 48. |
| and ... |
| In the numerator: | U(5,5)48 | = | 5*U(1,1)48 | - | the 5-fold tertius of 48. |
| In the denominator: | U(-1,1)48 | = | | - | the quartus of 48. |
