82 is carréphylic - approach of √82 ~ 9.0553851381
Subsequent approximations of √82 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-82p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*81+1)/1 | rational: 163 | actual: 163 | ⇒ F=326 |
| Smallest non-trivial p: | 2*9/1 | rational: 18 | actual: 18 | ⇒ primus foldage=18 |
| v-value qt-blocks: | 92-82*12: | -1 | | |
| Number of series: | 19 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 163 | 53137 | ... |
| p | 0 | 18 | 5868 | ... |
| In the numerator: | U(1,163)326 | = | 1/2*U(2,326)326 | - | half the secundus of 326. |
| In the denominator: | U(0,18)326 | = | 18*U(0,1)326 | - | the 18-fold primus of 326. |
| as well as ... |
| In the numerator: | U(0,1476)326 | = | 1476*U(0,1)326 | - | the 82*18-fold primus of 326. |
| In the denominator: | U(1,163)326 | = | 1/2*U(2,326)326 | - | half the secundus of 326. |
| and ... |
| In the numerator: | U(-9,9)326 | = | 9*U(-1,1)326 | - | the 9-fold quartus of 326. |
| In the denominator: | U(1,1)326 | = | | - | the tertius of 326. |
