83 is carréphylic - approach of √83 ~ 9.1104335791
Subsequent approximations of √83 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-83p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*81+2)/2 | rational: 82 | actual: 82 | ⇒ F=164 |
| Smallest non-trivial p: | 2*9/2 | rational: 9 | actual: 9 | ⇒ primus foldage=9 |
| v-value qt-blocks: | 92-83*12: | -2 | | |
| Number of series: | 15 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,82)164 | = | 1/2*U(2,164)164 | - | half the secundus of 164. |
| In the denominator: | U(0,9)164 | = | 9*U(0,1)164 | - | the 9-fold primus of 164. |
| as well as ... |
| In the numerator: | U(0,747)164 | = | 747*U(0,1)164 | - | the 83*9-fold primus of 164. |
| In the denominator: | U(1,82)164 | = | 1/2*U(2,164)164 | - | half the secundus of 164. |
| and ... |
| In the numerator: | U(-9,9)164 | = | 9*U(-1,1)164 | - | the 9-fold quartus of 164. |
| In the denominator: | U(1,1)164 | = | | - | the tertius of 164. |
