42 is carréphylic - approach of √42 ~ 6.4807406984
Subsequent approximations of √42 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-42p2 = 1 | | | |
| d = distance to nearest square N2: | +6 | | | |
| Smallest non-trivial s: | (2*36+6)/6 | rational: 13 | actual: 13 | ⇒ F=26 |
| Smallest non-trivial p: | 2*6/6 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 62-42*12: | -6 | | |
| Number of series: | 8 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 13 | 337 | 8749 | 227137 | 5896813 | 153090001 | ... |
| p | 0 | 2 | 52 | 1350 | 35048 | 909898 | 23622300 | ... |
| In the numerator: | U(1,13)26 | = | 1/2*U(2,26)26 | - | half the secundus of 26. |
| In the denominator: | U(0,2)26 | = | 2*U(0,1)26 | - | the 2-fold primus of 26. |
| as well as ... |
| In the numerator: | U(0,84)26 | = | 84*U(0,1)26 | - | the 42*2-fold primus of 26. |
| In the denominator: | U(1,13)26 | = | 1/2*U(2,26)26 | - | half the secundus of 26. |
| and ... |
| In the numerator: | U(-6,6)26 | = | 6*U(-1,1)26 | - | the 6-fold quartus of 26. |
| In the denominator: | U(1,1)26 | = | | - | the tertius of 26. |
