68 is carréphylic - approach of √68=2√17 ~ 8.2462112512
Subsequent approximations of √68 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-68p2 = 1 | | | |
| d = distance to nearest square N2: | +4 | | | |
| Smallest non-trivial s: | (2*64+4)/4 | rational: 33 | actual: 33 | ⇒ F=66 |
| Smallest non-trivial p: | 2*8/4 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value qt-blocks: | 82-68*12: | -4 | | |
| Number of series: | 11 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 33 | 2177 | 143649 | ... |
| p | 0 | 4 | 264 | 17420 | ... |
| In the numerator: | U(1,33)66 | = | 1/2*U(2,66)66 | - | half the secundus of 66. |
| In the denominator: | U(0,4)66 | = | 4*U(0,1)66 | - | the 4-fold primus of 66. |
| as well as ... |
| In the numerator: | U(0,272)66 | = | 272*U(0,1)66 | - | the 68*4-fold primus of 66. |
| In the denominator: | U(1,33)66 | = | 1/2*U(2,66)66 | - | half the secundus of 66. |
| and ... |
| In the numerator: | U(-8,8)66 | = | 8*U(-1,1)66 | - | the 8-fold quartus of 66. |
| In the denominator: | U(1,1)66 | = | | - | the tertius of 66. |
