58 is carréphobic - approach of √58 ~ 7.6157731059
Subsequent approximations of √58 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-58p2 = 1 | | | |
| d = distance to nearest square N2: | -6 | | | |
| Smallest non-trivial s: | (2*64-6)/6 | rational: 122/6 | actual: 19603 | ⇒ F=39206 |
| Smallest non-trivial p: | 2*8/6 | rational: 16/6 | actual: 2574 | ⇒ primus foldage=2574 |
| v-value qt-blocks: | 992-58*132: | -1 | | |
| Number of series: | 27 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 19603 | 768555217 | ... |
| p | 0 | 2574 | 100916244 | ... |
| In the numerator: | U(1,19603)39206 | = | 1/2*U(2,39206)39206 | - | half the secundus of 39206. |
| In the denominator: | U(0,2574)39206 | = | 2574*U(0,1)39206 | - | the 2574-fold primus of 39206. |
| as well as ... |
| In the numerator: | U(0,149292)39206 | = | 149292*U(0,1)39206 | - | the 58*2574-fold primus of 39206. |
| In the denominator: | U(1,19603)39206 | = | 1/2*U(2,39206)39206 | - | half the secundus of 39206. |
| and ... |
| In the numerator: | U(-99,99)39206 | = | 99*U(-1,1)39206 | - | the 99-fold quartus of 39206. |
| In the denominator: | U(13,13)39206 | = | 13*U(1,1)39206 | - | the 13-fold tertius of 39206. |
