24 is carréphylic - approach of √24=2√6 ~ 4.8989794856
Subsequent approximations of √24 - the position of a fraction indicates whether it is over or under the root-value.
24 is one less than a square, so the exception mentioned in
on root approach applies: 49 and 10, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being
5 and
1 because
52-24*12 = 1 satisfies the diophantine equation.
| Diophantine equation: | s2-24p2 = 1 | | | |
| d = distance to nearest square N2: | -1 | | | |
| Smallest non-trivial s: | (2*25-1)/1 | rational: 49 | actual: 49 (5) | ⇒ F=98 (10) |
| Smallest non-trivial p: | 2*5/1 | rational: 10 | actual: 10 (1) | ⇒ primus foldage=10 (1) |
| v-value qt-blocks: | 42-24*12: | -8 | | |
| Number of series: | 6 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 5 | 49 | 485 | 4801 | 47525 | 470449 | 4656965 | 46099201 | ... |
| p | 0 | 1 | 10 | 99 | 980 | 9701 | 96030 | 950599 | 9409960 | ... |
| In the numerator: | U(1,5)10 | = | 1/2*U(2,10)10 | - | half the secundus of 10. |
| In the denominator: | U(0,1)10 | = | | - | the primus of 10. |
| as well as ... |
| In the numerator: | U(0,24)10 | = | 24*U(0,1)10 | - | the 24-fold primus of 10. |
| In the denominator: | U(1,5)10 | = | 1/2*U(2,10)10 | - | half the secundus of 10. |
| and ... |
| In the numerator: | U(-4,4)10 | = | 4*U(-1,1)10 | - | the 4-fold quartus of 10. |
| In the denominator: | U(1,1)10 | = | | - | the tertius of 10. |
