54 is carréphobic - approach of √54=3√6 ~ 7.3484692283
Subsequent approximations of √54 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-54p2 = 1 | | | |
| d = distance to nearest square N2: | +5 | | | |
| Smallest non-trivial s: | (2*49+5)/5 | rational: 103/5 | actual: 485 | ⇒ F=970 |
| Smallest non-trivial p: | 2*7/5 | rational: 14/5 | actual: 66 | ⇒ primus foldage=66 |
| v-value qt-blocks: | 222-54*32: | -2 | | |
| Number of series: | 16 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 485 | 470449 | 456335045 | ... |
| p | 0 | 66 | 64020 | 470449 | ... |
| In the numerator: | U(1,485)970 | = | 1/2*U(2,970)970 | - | half the secundus of 970. |
| In the denominator: | U(0,66)970 | = | 66*U(0,1)970 | - | the 66-fold primus of 970. |
| as well as ... |
| In the numerator: | U(0,3564)970 | = | 3564*U(0,1)970 | - | the 54*66-fold primus of 970. |
| In the denominator: | U(1,485)970 | = | 1/2*U(2,970)970 | - | half the secundus of 970. |
| and ... |
| In the numerator: | U(-22,22)970 | = | 22*U(-1,1)970 | - | the 22-fold quartus of 970. |
| In the denominator: | U(3,3)970 | = | 3*U(1,1)970 | - | the 3-fold tertius of 970. |
