70 is carréphobic - approach of √70 ~ 8.3666002653
Subsequent approximations of √70 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-70p2 = 1 | | | |
| d = distance to nearest square N2: | +6 | | | |
| Smallest non-trivial s: | (2*64+6)/6 | rational: 134/6 | actual: 251 | ⇒ F=502 |
| Smallest non-trivial p: | 2*8/6 | rational: 16/6 | actual: 30 | ⇒ primus foldage=30 |
| v-value qt-blocks: | 252-70*32: | -5 | | |
| Number of series: | 15 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 251 | 126001 | 63252251 | ... |
| p | 0 | 30 | 15060 | 7560090 | ... |
| In the numerator: | U(1,251)502 | = | 1/2*U(2,502)502 | - | half the secundus of 502. |
| In the denominator: | U(0,30)502 | = | 30*U(0,1)502 | - | the 30-fold primus of 502. |
| as well as ... |
| In the numerator: | U(0,2100)502 | = | 2100*U(0,1)502 | - | the 70*30-fold primus of 502. |
| In the denominator: | U(1,251)502 | = | 1/2*U(2,502)502 | - | half the secundus of 502. |
| and ... |
| In the numerator: | U(-25,25)502 | = | 25*U(-1,1)502 | - | the 25-fold quartus of 502. |
| In the denominator: | U(3,3)502 | = | 3*U(1,1)502 | - | the 3-fold tertius of 502. |
