56 is carréphylic - approach of √56=2√14 ~ 7.4833147735
Subsequent approximations of √56 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-56p2 = 1 | | | |
| d = distance to nearest square N2: | +7 | | | |
| Smallest non-trivial s: | (2*49+7)/7 | rational: 15 | actual: 15 | ⇒ F=30 |
| Smallest non-trivial p: | 2*7/7 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 72-56*12: | -7 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 15 | 449 | 13455 | 403201 | 12082575 | 362074049 | ... |
| p | 0 | 2 | 60 | 1798 | 53880 | 1614602 | 48384180 | ... |
| In the numerator: | U(1,15)30 | = | 1/2*U(2,30)30 | - | half the secundus of 30. |
| In the denominator: | U(0,2)30 | = | 2*U(0,1)30 | - | the 2-fold primus of 30. |
| as well as ... |
| In the numerator: | U(0,112)30 | = | 112*U(0,1)30 | - | the 56*2-fold primus of 30. |
| In the denominator: | U(1,15)30 | = | 1/2*U(2,30)30 | - | half the secundus of 30. |
| and ... |
| In the numerator: | U(-7,7)30 | = | 7*U(-1,1)30 | - | the 7-fold quartus of 30. |
| In the denominator: | U(1,1)30 | = | | - | the tertius of 30. |
