71 is carréphobic - approach of √71 ~ 8.4261497732
Subsequent approximations of √71 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-71p2 = 1 | | | |
| d = distance to nearest square N2: | +7 | | | |
| Smallest non-trivial s: | (2*64+7)/7 | rational: 135/7 | actual: 3480 | ⇒ F=6960 |
| Smallest non-trivial p: | 2*8/7 | rational: 16/7 | actual: 413 | ⇒ primus foldage=413 |
| v-value tq-blocks: | 592-71*72: | +2 | | |
| Number of series: | 21 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 3480 | 24220799 | ... |
| p | 0 | 413 | 2874480 | ... |
| In the numerator: | U(1,3480)6960 | = | 1/2*U(2,6960)6960 | - | half the secundus of 6960. |
| In the denominator: | U(0,413)6960 | = | 413*U(0,1)6960 | - | the 413-fold primus of 6960. |
| as well as ... |
| In the numerator: | U(0,29323)6960 | = | 29323*U(0,1)6960 | - | the 71*413-fold primus of 6960. |
| In the denominator: | U(1,3480)6960 | = | 1/2*U(2,6960)6960 | - | half the secundus of 6960. |
| and ... |
| In the numerator: | U(59,59)6960 | = | 59*U(1,1)6960 | - | the 59-fold tertius of 6960. |
| In the denominator: | U(-7,7)6960 | = | 7*U(-1,1)6960 | - | the 7-fold quartus of 6960. |
