76 is carréphobic - approach of √76=2√19 ~ 8.7177978871
Subsequent approximations of √76 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-76p2 = 1 | | | |
| d = distance to nearest square N2: | -5 | | | |
| Smallest non-trivial s: | (2*81-5)/5 | rational: 157/5 | actual: 57799 | ⇒ F=115598 |
| Smallest non-trivial p: | 2*9/5 | rational: 18/5 | actual: 6630 | ⇒ primus foldage=6630 |
| v-value tq-blocks: | 3402-76*392: | +4 | | |
| v-value qt-blocks: | 7412-76*852: | -19 | | |
| Number of series: | 27 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 57799 | 6681448801 | ... |
| p | 0 | 6630 | 766414740 | ... |
| In the numerator: | U(1,57799)115598 | = | 1/2*U(2,115598)115598 | - | half the secundus of 115598. |
| In the denominator: | U(0,6630)115598 | = | 6630*U(0,1)115598 | - | the 6630-fold primus of 115598. |
| as well as ... |
| In the numerator: | U(0,503880)115598 | = | 503880*U(0,1)115598 | - | the 76*6630-fold primus of 115598. |
| In the denominator: | U(1,57799)115598 | = | 1/2*U(2,115598)115598 | - | half the secundus of 115598. |
| and ... |
| In the numerator: | U(340,340)115598 | = | 340*U(1,1)115598 | - | the 340-fold tertius of 115598. |
| In the denominator: | U(-39,39)115598 | = | 39*U(-1,1)115598 | - | the 39-fold quartus of 115598. |
| and ... |
| In the numerator: | U(-741,741)115598 | = | 741*U(-1,1)115598 | - | the 741-fold quartus of 115598. |
| In the denominator: | U(85,85)115598 | = | 85*U(1,1)115598 | - | the 85-fold tertius of 115598. |
