105 is carréphylic - approach of √105 ~ 10.2469507660
Subsequent approximations of √105 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-105p2 = 1 | | | |
| d = distance to nearest square N2: | +5 | | | |
| Smallest non-trivial s: | (2*100+5)/5 | rational: 41 | actual: 41 | ⇒ F=82 |
| Smallest non-trivial p: | 2*10/5 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value qt-blocks: | 102-105*12: | -5 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,41)82 | = | 1/2*U(2,82)82 | - | half the secundus of 82. |
| In the denominator: | U(0,4)82 | = | 4*U(0,1)82 | - | the 4-fold primus of 82. |
| as well as ... |
| In the numerator: | U(0,420)82 | = | 420*U(0,1)82 | - | the 105*4-fold primus of 82. |
| In the denominator: | U(1,41)82 | = | 1/2*U(2,82)82 | - | half the secundus of 82. |
| and ... |
| In the numerator: | U(-10,10)82 | = | 10*U(-1,1)82 | - | the 10-fold quartus of 82. |
| In the denominator: | U(1,1)82 | = | | - | the tertius of 82. |
