29 is carréphobic - approach of √29 ~ 5.3851648071
Subsequent approximations of √29 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-29p2 = 1 | | | |
| d = distance to nearest square N2: | +4 | | | |
| Smallest non-trivial s: | (2*25+4)/4 | rational: 54/4 | actual: 9801 | ⇒ F=19602 |
| Smallest non-trivial p: | 2*5/4 | rational: 10/4 | actual: 1820 | ⇒ primus foldage=1820 |
| v-value qt-blocks: | 702-29*132: | -1 | | |
| Number of series: | 21 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 9801 | 192119201 | ... |
| p | 0 | 1820 | 35675640 | ... |
| In the numerator: | U(1,9801)19602 | = | 1/2*U(2,19602)19602 | - | half the secundus of 19602. |
| In the denominator: | U(0,1820)19602 | = | 1820*U(0,1)19602 | - | the 1820-fold primus of 19602. |
| as well as ... |
| In the numerator: | U(0,52780)19602 | = | 52780*U(0,1)19602 | - | the 29*1820-fold primus of 19602. |
| In the denominator: | U(1,9801)19602 | = | 1/2*U(2,19602)19602 | - | half the secundus of 19602. |
| and ... |
| In the numerator: | U(-70,70)19602 | = | 70*U(-1,1)19602 | - | the 70-fold quartus of 19602. |
| In the denominator: | U(13,13)19602 | = | 13*U(1,1)19602 | - | the 13-fold tertius of 19602. |
