41 is carréphobic - approach of √41 ~ 6.4031242374
Subsequent approximations of √41 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-41p2 = 1 | | | |
| d = distance to nearest square N2: | +5 | | | |
| Smallest non-trivial s: | (2*36+5)/5 | rational: 77/5 | actual: 2049 | ⇒ F=4098 |
| Smallest non-trivial p: | 2*6/5 | rational: 12/5 | actual: 320 | ⇒ primus foldage=320 |
| v-value qt-blocks: | 322-41*52: | -1 | | |
| Number of series: | 19 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 2049 | 8396801 | 34410088449 | ... |
| p | 0 | 320 | 1311360 | 5373952960 | ... |
| In the numerator: | U(1,2049)4098 | = | 1/2*U(2,4098)4098 | - | half the secundus of 4098. |
| In the denominator: | U(0,320)4098 | = | 320*U(0,1)4098 | - | the 320-fold primus of 4098. |
| as well as ... |
| In the numerator: | U(0,13120)3040 | = | 13120*U(0,1)4098 | - | the 41*320-fold primus of 4098. |
| In the denominator: | U(1,2049)4098 | = | 1/2*U(2,4098)4098 | - | half the secundus of 4098. |
| and ... |
| In the numerator: | U(-32,32)4098 | = | 32*U(-1,1)4098 | - | the 32-fold quartus of 4098. |
| In the denominator: | U(5,5)4098 | = | 5*U(1,1)4098 | - | the 5-fold tertius of 4098. |
