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105 is carréphylic - approach of √105 ~ 10.2469507660

Subsequent approximations of √105 - 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 31 41 420 461 502 543 584 625 666 707 748 789 830 2531 3361 34440 ... 0 1 1 1 1 1 1 1 1 1 1 1 3 4 41 45 49 53 57 61 65 69 73 77 81 247 328 3361 ...

 Diophantine equation: s2-105p2 = 1 d = distance to nearest square N2: +5 Smallest non-trivial s: (2*100+5)/5 rational: 41 actual: 41 ⇒ F=82 Smallest non-trivial p: 2*10/5 rational: 4 actual: 4 ⇒ primus foldage=4 v-value qt-blocks: 102-105*12: -5 Number of series: 13

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 41 3361 ... p 0 4 328 ...

 In the numerator: U(1,41)82 = 1/2*U(2,82)82 - half the secundus of 82. In the denominator: U(0,4)82 = 4*U(0,1)82 - the 4-fold primus of 82. as well as ... In the numerator: U(0,420)82 = 420*U(0,1)82 - the 105*4-fold primus of 82. In the denominator: U(1,41)82 = 1/2*U(2,82)82 - half the secundus of 82. and ... In the numerator: U(-10,10)82 = 10*U(-1,1)82 - the 10-fold quartus of 82. In the denominator: U(1,1)82 = - the tertius of 82.