45 is carréphobic - approach of √45=3√5 ~ 6.7082039325
Subsequent approximations of √45 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-45p2 = 1 | | | |
| d = distance to nearest square N2: | -4 | | | |
| Smallest non-trivial s: | (2*49-4)/4 | rational: 94/4 | actual: 161 | ⇒ F=322 |
| Smallest non-trivial p: | 2*7/4 | rational: 14/4 | actual: 24 | ⇒ primus foldage=24 |
| v-value qt-blocks: | 202-45*32: | -5 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 2049 | 8396801 | 34410088449 | ... |
| p | 0 | 320 | 1311360 | 5373952960 | ... |
| In the numerator: | U(1,161)322 | = | 1/2*U(2,322)322 | - | half the secundus of 322. |
| In the denominator: | U(0,24)322 | = | 24*U(0,1)322 | - | the 24-fold primus of 322. |
| as well as ... |
| In the numerator: | U(0,1080)322 | = | 1080*U(0,1)322 | - | the 45*24-fold primus of 322. |
| In the denominator: | U(1,161)322 | = | 1/2*U(2,322)322 | - | half the secundus of 322. |
| and ... |
| In the numerator: | U(-20,20)322 | = | 20*U(-1,1)322 | - | the 20-fold quartus of 322. |
| In the denominator: | U(3,3)322 | = | 3*U(1,1)322 | - | the 3-fold tertius of 322. |
