65 is carréphylic - approach of √65 ~ 8.0622577483
Subsequent approximations of √65 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-65p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*64+1)/1 | rational: 129 | actual: 129 | ⇒ F=258 |
| Smallest non-trivial p: | 2*8/1 | rational: 16 | actual: 16 | ⇒ primus foldage=16 |
| v-value qt-blocks: | 82-65*12: | -1 | | |
| Number of series: | 17 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 129 | 33281 | ... |
| p | 0 | 16 | 4128 | ... |
| In the numerator: | U(1,129)258 | = | 1/2*U(2,258)258 | - | half the secundus of 258. |
| In the denominator: | U(0,16)258 | = | 16*U(0,1)1258 | - | the 16-fold primus of 258. |
| as well as ... |
| In the numerator: | U(0,1040)258 | = | 1040*U(0,1)258 | - | the 65*16-fold primus of 258. |
| In the denominator: | U(1,129)258 | = | 1/2*U(2,258)258 | - | half the secundus of 258. |
| and ... |
| In the numerator: | U(-8,8)258 | = | 8*U(-1,1)258 | - | the 8-fold quartus of 258. |
| In the denominator: | U(1,1)258 | = | | - | the tertius of 258. |
