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91 is carréphobic - approach of √91 ~ 9.5393920142

Subsequent approximations of √91 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 6 7 8 9 10 19 67 86 105 124 477 601 725 849 1574 15015 16589 18163 19737 21311 22885 24459 26033 27607 29181 30755 59936 210563 270499 330435 390371 1501548 1891919 2282290 2672661 4954951 47267220 ... 0 1 1 1 1 1 1 1 1 1 1 1 2 7 9 11 13 50 63 76 89 165 1574 1739 1904 2069 2234 2399 2564 2729 2894 3059 3224 6283 22073 28356 34639 40922 157405 198327 239249 280171 519420 4954951 ...

 Diophantine equation: s2-91p2 = 1 d = distance to nearest square N2: -9 Smallest non-trivial s: (2*100-9)/9 rational: 191/9 actual: 1574 ⇒ F=3148 Smallest non-trivial p: 2*10/9 rational: 20/9 actual: 165 ⇒ primus foldage=165 v-value qt-blocks: 1052-91*112: +14 Number of series: 21

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 1574 4954951 ... p 0 165 519420 ...

 In the numerator: U(1,1574)3148 = 1/2*U(2, 3148)3148 - half the secundus of 3148. In the denominator: U(0,165)3148 = 165*U(0,1)3148 - the 165-fold primus of 3148. as well as ... In the numerator: U(0,15015)3148 = 15015*U(0,1)3148 - the 91*165-fold primus of 3148. In the denominator: U(1,1574)3148 = 1/2*U(2,3148)3148 - half the secundus of 3148. and ... In the numerator: U(105,105)3148 = 105*U(1,1)3148 - the 105-fold tertius of 3148. In the denominator: U(-11,11)3148 = 11*U(-1,1)3148 - the 11-fold quartus of 3148.