92 is carréphobic - approach of √92=2√23 ~ 9.5916630466
Subsequent approximations of √92 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-92p2 = 1 | | | |
| d = distance to nearest square N2: | -8 | | | |
| Smallest non-trivial s: | (2*100-8)/8 | rational: 24 | actual: 1151 | ⇒ F=2302 |
| Smallest non-trivial p: | 2*10/8 | rational: 20/8 | actual: 120 | ⇒ primus foldage=120 |
| v-value tq-blocks: | 482-92*52: | +4 | | |
| v-value qt-blocks: | 1152-92*122: | -23 | | |
| Number of series: | 20 | | | |
Note that the 'rational s' is an integer, but the 'rational p' is not.
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 1151 | 2649601 | ... |
| p | 0 | 120 | 276240 | ... |
| In the numerator: | U(1,1151)2302 | = | 1/2*U(2,2302)2302 | - | half the secundus of 2302. |
| In the denominator: | U(0,120)2302 | = | 120*U(0,1)2302 | - | the 120-fold primus of 2302. |
| as well as ... |
| In the numerator: | U(0,11040)2302 | = | 11040*U(0,1)2302 | - | the 92*120-fold primus of 2302. |
| In the denominator: | U(1,1151)2302 | = | 1/2*U(2,2302)2302 | - | half the secundus of 2302. |
| and ... |
| In the numerator: | U(48,48)2302 | = | 48*U(1,1)2302 | - | the 48-fold tertius of 2302. |
| In the denominator: | U(-5,5)2302 | = | 5*U(-1,1)2302 | - | the 5-fold quartus of 2302. |
| and ... |
| In the numerator: | U(-115,115)2302 | = | 115*U(-1,1)2302 | - | the 115-fold quartus of 2302. |
| In the denominator: | U(12,12)2302 | = | 12*U(1,1)2302 | - | the 12-fold tertius of 2302. |
