59 is carréphobic - approach of √59 ~ 7.6811457479
Subsequent approximations of √59 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-59p2 = 1 | | | |
| d = distance to nearest square N2: | -5 | | | |
| Smallest non-trivial s: | (2*64-5)/5 | rational: 123/5 | actual: 530 | ⇒ F=1060 |
| Smallest non-trivial p: | 2*8/5 | rational: 16/5 | actual: 69 | ⇒ primus foldage=69 |
| v-value qt-blocks: | 232-59*32: | -2 | | |
| Number of series: | 17 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 530 | 561799 | 595506410 | ... |
| p | 0 | 69 | 73140 | 77528331 | ... |
| In the numerator: | U(1,530)1060 | = | 1/2*U(2,1060)1060 | - | half the secundus of 1060. |
| In the denominator: | U(0,69)1060 | = | 69*U(0,1)1060 | - | the 69-fold primus of 1060. |
| as well as ... |
| In the numerator: | U(0,4071)1060 | = | 4071*U(0,1)1060 | - | the 59*69-fold primus of 1060. |
| In the denominator: | U(1,530)1060 | = | 1/2*U(2,1060)1060 | - | half the secundus of 1060. |
| and ... |
| In the numerator: | U(-23,23)1060 | = | 23*U(-1,1)1060 | - | the 23-fold quartus of 1060. |
| In the denominator: | U(3,3)1060 | = | 3*U(1,1)1060 | - | the 3-fold tertius of 1060. |
