67 is carréphobic - approach of √67 ~ 8.1853527719
Subsequent approximations of √67 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-67p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*64+3)/3 | rational: 131/3 | actual: 48842 | ⇒ F=97684 |
| Smallest non-trivial p: | 2*8/3 | rational: 16/3 | actual: 5967 | ⇒ primus foldage=5967 |
| v-value qt-blocks: | 2212-67*272: | -2 | | |
| Number of series: | 26 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 48842 | 4771081927 | ... |
| p | 0 | 5967 | 582880428 | ... |
| In the numerator: | U(1,48842)97684 | = | 1/2*U(2,97684)97684 | - | half the secundus of 97684. |
| In the denominator: | U(0,5967)97684 | = | 5967*U(0,1)97684 | - | the 5967-fold primus of 97684. |
| as well as ... |
| In the numerator: | U(0,399789)97684 | = | 399789*U(0,1)97684 | - | the 67*5967-fold primus of 97684. |
| In the denominator: | U(1,48842)97684 | = | 1/2*U(2,97684)97684 | - | half the secundus of 97684. |
| and ... |
| In the numerator: | U(-221,221)97684 | = | 221*U(-1,1)97684 | - | the 221-fold quartus of 97684. |
| In the denominator: | U(27,27)97684 | = | 27*U(1,1)97684 | - | the 27-fold tertius of 97684. |
