50 is carréphylic - approach of √50=5√2 ~ 7.0710678119
Subsequent approximations of √50 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-50p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*49+1)/1 | rational: 99 | actual: 99 | ⇒ F=198 |
| Smallest non-trivial p: | 2*7/1 | rational: 14 | actual: 14 | ⇒ primus foldage=14 |
| v-value qt-blocks: | 72-50*12: | -1 | | |
| Number of series: | 15 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 99 | 19601 | 3880899 | 768398401 | ... |
| p | 0 | 14 | 2772 | 548842 | 108667944 | ... |
| In the numerator: | U(1,99)198 | = | 1/2*U(2,198)198 | - | half the secundus of 198. |
| In the denominator: | U(0,14)198 | = | 14*U(0,1)198 | - | the 14-fold primus of 198. |
| as well as ... |
| In the numerator: | U(0,700)198 | = | 700*U(0,1)198 | - | the 50*14-fold primus of 198. |
| In the denominator: | U(1,99)198 | = | 1/2*U(2,198)198 | - | half the secundus of 198. |
| and ... |
| In the numerator: | U(-7,7)198 | = | 7*U(-1,1)198 | - | the 7-fold quartus of 198. |
| In the denominator: | U(1,1)198 | = | | - | the tertius of 198. |
