77 is carréphobic - approach of √77 ~ 8.7749643874
Subsequent approximations of √77 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-77p2 = 1 | | | |
| d = distance to nearest square N2: | -4 | | | |
| Smallest non-trivial s: | (2*81-4)/4 | rational: 158/4 | actual: 351 | ⇒ F=702 |
| Smallest non-trivial p: | 2*9/4 | rational: 18/4 | actual: 40 | ⇒ primus foldage=40 |
| v-value qt-blocks: | 352-77*42: | -7 | | |
| Number of series: | 16 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 351 | 246401 | ... |
| p | 0 | 40 | 28080 | ... |
| In the numerator: | U(1,351)702 | = | 1/2*U(2,702)702 | - | half the secundus of 702. |
| In the denominator: | U(0,40)702 | = | 40*U(0,1)702 | - | the 40-fold primus of 702. |
| as well as ... |
| In the numerator: | U(0,3080)702 | = | 3080*U(0,1)702 | - | the 77*40-fold primus of 702. |
| In the denominator: | U(1,351)702 | = | 1/2*U(2,702)702 | - | half the secundus of 702. |
| and ... |
| In the numerator: | U(-35,35)702 | = | 35*U(-1,1)702 | - | the 35-fold quartus of 702. |
| In the denominator: | U(4,4)702 | = | 4*U(1,1)702 | - | the 4-fold tertius of 702. |
