107 is carréphobic - approach of √107 ~ 10.3440804328
Subsequent approximations of √107 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-107p2 = 1 | | | |
| d = distance to nearest square N2: | +7 | | | |
| Smallest non-trivial s: | (2*100+7)/7 | rational: 207/7 | actual: 962 | ⇒ F=1924 |
| Smallest non-trivial p: | 2*10/7 | rational: 20/7 | actual: 93 | ⇒ primus foldage=93 |
| v-value qt-blocks: | 312-107*32: | -2 | | |
| Number of series: | 21 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 962 | 1850887 | ... |
| p | 0 | 93 | 178932 | ... |
| In the numerator: | U(1,968)1924 | = | 1/2*U(2,1924)1924 | - | half the secundus of 1924. |
| In the denominator: | U(0,93)1924 | = | 93*U(0,1)1924 | - | the 93-fold primus of 1924. |
| as well as ... |
| In the numerator: | U(0,9951)1924 | = | 9951*U(0,1)1924 | - | the 107*93-fold primus of 1924. |
| In the denominator: | U(1,968)1924 | = | 1/2*U(2,1924)1924 | - | half the secundus of 1924. |
| and ... |
| In the numerator: | U(-31,31)1924 | = | 31*U(-1,1)1924 | - | the 31-fold quartus of 1924. |
| In the denominator: | U(3,3)1924 | = | 3*U(1,1)1924 | - | the 3-fold tertius of 1924. |
