103 is carréphobic - approach of √103 ~ 10.1488915651
Using the
incremental profile, the questionmarks can be filled in - the position of a fraction indicates whether it is over or under the root-value. The positioning of the missing fractions corresponds to the first section.
Subsequent approximations of √103.
| Diophantine equation: | s2-103p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*100+3)/3 | rational: 203/3 | actual: 227528 | ⇒ F=455056 |
| Smallest non-trivial p: | 2*10/3 | rational: 20/3 | actual: 22419 | ⇒ primus foldage=22419 |
| v-value tq-blocks: | 4772-103*472: | +2 | | |
| Number of series: | 32 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 227528 | 103537981568 | ... |
| p | 0 | 22419 | 10201900464 | ... |
| In the numerator: | U(1,227528)455056 | = | 1/2*U(2,455056)455056 | - | half the secundus of 455056. |
| In the denominator: | U(0,22419)455056 | = | 22419*U(0,1)455056 | - | the 22419-fold primus of 455056. |
| as well as ... |
| In the numerator: | U(0,2309157)455056 | = | 2309157*U(0,1)455056 | - | the 103*22419-fold primus of 455056. |
| In the denominator: | U(1,227528)455056 | = | 1/2*U(2,455056)455056 | - | half the secundus of 455056. |
| and ... |
| In the numerator: | U(477,477)455056 | = | 477*U(1,1)455056 | - | the 477-fold tertius of 455056. |
| In the denominator: | U(-47,47)455056 | = | 47*U(-1,1)455056 | - | the 47-fold quartus of 455056. |
