53 is carréphobic - approach of √53 ~ 7.2801098893
Subsequent approximations of √53 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-53p2 = 1 | | | |
| d = distance to nearest square N2: | +4 | | | |
| Smallest non-trivial s: | (2*49+4)/4 | rational: 102/4 | actual: 66249 | ⇒ F=132498 |
| Smallest non-trivial p: | 2*7/4 | rational: 14/4 | actual: 9100 | ⇒ primus foldage=9100 |
| v-value qt-blocks: | 1822-53*252: | -1 | | |
| Number of series: | 27 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 66249 | 8777860001 | ... |
| p | 0 | 9100 | 1205731800 | ... |
| In the numerator: | U(1,66249)132498 | = | 1/2*U(2,132498)132498 | - | half the secundus of 132498. |
| In the denominator: | U(0,9100)132498 | = | 9100*U(0,1)132498 | - | the 9100-fold primus of 132498. |
| as well as ... |
| In the numerator: | U(0,482300)132498 | = | 482300*U(0,1)132498 | - | the 53*9100-fold primus of 132498. |
| In the denominator: | U(1,66249)132498 | = | 1/2*U(2,132498)132498 | - | half the secundus of 132498. |
| and ... |
| In the numerator: | U(-182,182)132498 | = | 182*U(-1,1)132498 | - | the 182-fold quartus of 132498. |
| In the denominator: | U(25,25)132498 | = | 25*U(1,1)132498 | - | the 25-fold tertius of 132498. |
