31 is carréphobic - approach of √31 ~ 5.5677643628
Subsequent approximations of √31 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-31p2 = 1 | | | |
| d = distance to nearest square N2: | -5 | | | |
| Smallest non-trivial s: | (2*36-5)/4 | rational: 67/5 | actual: 1520 | ⇒ F=3040 |
| Smallest non-trivial p: | 2*6/5 | rational: 12/5 | actual: 273 | ⇒ primus foldage=273 |
| v-value tq-blocks: | 392-31*72: | +2 | | |
| Number of series: | 17 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 1520 | 4620799 | ... |
| p | 0 | 273 | 829920 | ... |
| In the numerator: | U(1,1520)3040 | = | 1/2*U(2,3040)3040 | - | half the secundus of 3040. |
| In the denominator: | U(0,273)3040 | = | 273*U(0,1)3040 | - | the 273-fold primus of 3040. |
| as well as ... |
| In the numerator: | U(0,8463)3040 | = | 8463*U(0,1)3040 | - | the 31*273-fold primus of 3040. |
| In the denominator: | U(1,1520)3040 | = | 1/2*U(2,3040)3040 | - | half the secundus of 3040. |
| and ... |
| In the numerator: | U(39,39)3040 | = | 39*U(1,1)3040 | - | the 39-fold tertius of 3040. |
| In the denominator: | U(-7,7)3040 | = | 7*U(-1,1)3040 | - | the 7-fold quartus of 3040. |
