91 is carréphobic - approach of √91 ~ 9.5393920142
Subsequent approximations of √91 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-91p2 = 1 | | | |
| d = distance to nearest square N2: | -9 | | | |
| Smallest non-trivial s: | (2*100-9)/9 | rational: 191/9 | actual: 1574 | ⇒ F=3148 |
| Smallest non-trivial p: | 2*10/9 | rational: 20/9 | actual: 165 | ⇒ primus foldage=165 |
| v-value qt-blocks: | 1052-91*112: | +14 | | |
| Number of series: | 21 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 1574 | 4954951 | ... |
| p | 0 | 165 | 519420 | ... |
| In the numerator: | U(1,1574)3148 | = | 1/2*U(2, 3148)3148 | - | half the secundus of 3148. |
| In the denominator: | U(0,165)3148 | = | 165*U(0,1)3148 | - | the 165-fold primus of 3148. |
| as well as ... |
| In the numerator: | U(0,15015)3148 | = | 15015*U(0,1)3148 | - | the 91*165-fold primus of 3148. |
| In the denominator: | U(1,1574)3148 | = | 1/2*U(2,3148)3148 | - | half the secundus of 3148. |
| and ... |
| In the numerator: | U(105,105)3148 | = | 105*U(1,1)3148 | - | the 105-fold tertius of 3148. |
| In the denominator: | U(-11,11)3148 | = | 11*U(-1,1)3148 | - | the 11-fold quartus of 3148. |
