21 is carréphobic - approach of √21 ~ 4.5825756950
Subsequent approximations of √21 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-21p2 = 1 | | | |
| d = distance to nearest square N2: | -4 | | | |
| Smallest non-trivial s: | (2*25-4)/4 | rational: 46/4 | actual: 55 | ⇒ F=110 |
| Smallest non-trivial p: | 2*5/4 | rational: 10/4 | actual: 12 | ⇒ primus foldage=12 |
| v-value qt-blocks: | 92-21*22: | -3 | | |
| Number of series: | 10 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 55 | 6049 | 665335 | 73180801 | ... |
| p | 0 | 12 | 1320 | 145188 | 15969360 | ... |
| In the numerator: | U(1,55)110 | = | 1/2*U(2,110)110 | - | half the secundus of 110. |
| In the denominator: | U(0,12)110 | = | 12*U(0,1)110 | - | the 12-fold primus of 110. |
| as well as ... |
| In the numerator: | U(0,252)110 | = | 252*U(0,1)110 | - | the 21*12-fold primus of 110. |
| In the denominator: | U(1,55)110 | = | 1/2*U(2,110)110 | - | half the secundus of 110. |
| and ... |
| In the numerator: | U(-9,9)110 | = | 9*U(-1,1)110 | - | the 9-fold quartus of 110. |
| In the denominator: | U(2,2)110 | = | 2*U(1,1)110 | - | the 2-fold tertius of 110. |
