46 is carréphobic - approach of √46 ~ 6.7823299831
Subsequent approximations of √46 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-46p2 = 1 | | | |
| d = distance to nearest square N2: | -3 | | | |
| Smallest non-trivial s: | (2*49-3)/3 | rational: 95/3 | actual: 24335 | ⇒ F=48670 |
| Smallest non-trivial p: | 2*7/3 | rational: 14/3 | actual: 3588 | ⇒ primus foldage=3588 |
| v-value tq-blocks: | 1562-46*232: | +2 | | |
| v-value qt-blocks: | 5292-46*782: | -23 | | |
| Number of series: | 24 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 24335 | 1184384449 | ... |
| p | 0 | 3588 | 174627960 | ... |
| In the numerator: | U(1,24335)48670 | = | 1/2*U(2,48670)48670 | - | half the secundus of 48670. |
| In the denominator: | U(0,3588)48670 | = | 3588*U(0,1)48670 | - | the 3588-fold primus of 48670. |
| as well as ... |
| In the numerator: | U(0,165048)48670 | = | 165048*U(0,1)48670 | - | the 46*3588-fold primus of 48670. |
| In the denominator: | U(1,24335)48670 | = | 1/2*U(2,48670)48670 | - | half the secundus of 48670. |
| and ... |
| In the numerator: | U(156,156)48670 | = | 156*U(1,1)48670 | - | the 156-fold tertius of 48670. |
| In the denominator: | U(-23,23)48670 | = | 23*U(-1,1)48670 | - | the 23-fold quartus of 48670. |
| and ... |
| In the numerator: | U(-529,529)48670 | = | 529*U(-1,1)48670 | - | the 529-fold quartus of 48670. |
| In the denominator: | U(78,78)48670 | = | 78*U(1,1)48670 | - | the 78-fold tertius of 48670. |
