39 is carréphylic - approach of √39 ~ 6.2449979984
Subsequent approximations of √39 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-39p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*36+3)/3 | rational: 25 | actual: 25 | ⇒ F=50 |
| Smallest non-trivial p: | 2*6/3 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value qt-blocks: | 62-39*12: | -3 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 25 | 1249 | 62425 | 3120001 | 155937625 | ... |
| p | 0 | 4 | 200 | 9996 | 499600 | 24970004 | ... |
| In the numerator: | U(1,25)50 | = | 1/2*U(2,50)50 | - | half the secundus of 50. |
| In the denominator: | U(0,4)50 | = | 4*U(0,1)50 | - | the 4-fold primus of 50. |
| as well as ... |
| In the numerator: | U(0,156)50 | = | 156*U(0,1)50 | - | the 39*4-fold primus of 50. |
| In the denominator: | U(1,25)50 | = | 1/2*U(2,50)50 | - | half the secundus of 50. |
| and ... |
| In the numerator: | U(-6,6)50 | = | 6*U(-1,1)50 | - | the 6-fold quartus of 50. |
| In the denominator: | U(1,1)50 | = | | - | the tertius of 50. |
