84 is carréphylic - approach of √84=2√21 ~ 9.1651513899
Subsequent approximations of √84 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-84p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*81+3)/3 | rational: 55 | actual: 55 | ⇒ F=110 |
| Smallest non-trivial p: | 2*9/3 | rational: 6 | actual: 6 | ⇒ primus foldage=6 |
| v-value qt-blocks: | 92-84*12: | -3 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,55)110 | = | 1/2*U(2,110)110 | - | half the secundus of 110. |
| In the denominator: | U(0,6)110 | = | 6*U(0,1)110 | - | the 6-fold primus of 110. |
| as well as ... |
| In the numerator: | U(0,504)110 | = | 504*U(0,1)110 | - | the 84*6-fold primus of 110. |
| In the denominator: | U(1,55)110 | = | 1/2*U(2,110)110 | - | half the secundus of 110. |
| and ... |
| In the numerator: | U(-9,9)110 | = | 9*U(-1,1)110 | - | the 9-fold quartus of 110. |
| In the denominator: | U(1,1)110 | = | | - | the tertius of 106. |
