### Who's Online

We have 60 guests and no members online

5 is carréphylic - approach of √35 ~ 5.9160797831

Subsequent approximations of √35 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 6 35 41 47 53 59 65 71 420 491 562 633 704 775 846 5005 5851 6697 7543 8389 9235 10081 59640 69721 79802 89883 99964 110045 120126 710675 830801 950927 1071053 1191179 1311305 1431431 8468460 9899891 11331322 12762753 14194184 15625615 17057046 100910845 ... 0 1 1 1 1 1 1 1 6 7 8 9 10 11 12 71 83 95 107 119 131 143 846 989 1132 1275 1418 1561 1704 10081 11785 13489 15193 16897 18601 20305 120126 140431 160736 181041 201346 221651 241956 1431431 1673387 1915343 2157299 2399255 2641211 2883167 17057046 ...

35 is one less than a square, so the exception mentioned in on root approach applies: 71 and 12, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being 6 and 1 because 62-35*12 = 1 satisfies the diophantine equation.
 Diophantine equation: s2-35p2 = 1 d = distance to nearest square N2: -1 Smallest non-trivial s: (2*36-1)/1 rational: 71 actual: 71 (6) ⇒ F=142 (12) Smallest non-trivial p: 2*6/1 rational: 12 actual: 12 (1) ⇒ primus foldage=12 (1) v-value qt-blocks: 52-35*12: -10 Number of series: 7

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 6 71 846 10081 120126 1431431 17057046 ... p 0 1 12 143 1704 20305 241956 2883167 ...

 In the numerator: U(1,6)12 = 1/2*U(2,12)12 - half the secundus of 12. In the denominator: U(0,1)12 = - the primus of 12. as well as ... In the numerator: U(0,35)12 = 35*U(0,1)12 - the 35-fold primus of 12. In the denominator: U(1,6)12 = 1/2*U(2,12)12 - half the secundus of 12. and ... In the numerator: U(-5,5)12 = 5*U(-1,1)12 - the 5-fold quartus of 12. In the denominator: U(1,1)12 = - the tertius of 12.