43 is carréphobic - approach of √43 ~ 6.5574385243
Subsequent approximations of √43 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-43p2 = 1 | | | |
| d = distance to nearest square N2: | -6 | | | |
| Smallest non-trivial s: | (2*49-6)/6 | rational: 92/6 | actual: 3482 | ⇒ F=6964 |
| Smallest non-trivial p: | 2*7/6 | rational: 14/6 | actual: 531 | ⇒ primus foldage=531 |
| v-value qt-blocks: | 592-43*92: | -2 | | |
| Number of series: | 20 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 3482 | 24248647 | ... |
| p | 0 | 531 | 3697884 | ... |
| In the numerator: | U(1,3482)6964 | = | 1/2*U(2,6964)6964 | - | half the secundus of 6964. |
| In the denominator: | U(0,531)6964 | = | 531*U(0,1)6964 | - | the 531-fold primus of 6964. |
| as well as ... |
| In the numerator: | U(0,22833)6964 | = | 22833*U(0,1)6964 | - | the 43*531-fold primus of 6964. |
| In the denominator: | U(1,3482)6964 | = | 1/2*U(2,6964)6964 | - | half the secundus of 6964. |
| and ... |
| In the numerator: | U(-59,59)6964 | = | 59*U(-1,1)6964 | - | the 59-fold quartus of 6964. |
| In the denominator: | U(9,9)6964 | = | 9*U(1,1)6964 | - | the 9-fold tertius of 6964. |
