78 is carréphylic - approach of √78 ~ 8.8317608663
Subsequent approximations of √78 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-78p2 = 1 | | | |
| d = distance to nearest square N2: | -3 | | | |
| Smallest non-trivial s: | (2*81-3)/3 | rational: 53 | actual: 53 | ⇒ F=106 |
| Smallest non-trivial p: | 2*9/3 | rational: 6 | actual: 6 | ⇒ primus foldage=6 |
| v-value tq-blocks: | 92-78*12: | +3 | | |
| v-value qt-blocks: | 262-78*32: | -26 | | |
| Number of series: | 14 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,53)106 | = | 1/2*U(2,106)106 | - | half the secundus of 106. |
| In the denominator: | U(0,6)106 | = | 6*U(0,1)106 | - | the 6-fold primus of 106. |
| as well as ... |
| In the numerator: | U(0,468)106 | = | 468*U(0,1)106 | - | the 78*6-fold primus of 106. |
| In the denominator: | U(1,53)106 | = | 1/2*U(2,106)106 | - | half the secundus of 106. |
| and ... |
| In the numerator: | U(9,9)106 | = | 9*U(1,1)106 | - | the 9-fold tertius of 106. |
| In the denominator: | U(-1,1)106 | = | | - | the quartus of 106. |
| and ... |
| In the numerator: | U(-26,26)106 | = | 26*U(-1,1)106 | - | the 26-fold quartus of 106. |
| In the denominator: | U(3,3)106 | = | 3*U(1,1)106 | - | the 3-fold tertius of 106. |
