A259684 - OEIS

%I #9 Jan 01 2021 04:28:10

%S 3,5,3,5,2,1,3,4,1,1,1,9,153,7,7,6,13,5,1,17,1,11,4,1,4,4,11,253,4,1,

%T 1,1,1,5,5,2,8,1,1,4,103,39,29,2,5,19,8,7,1,1,163,4,8,63,44,23,35,7,2,

%U 5,4,5,13,17,1,12,5,8,193,22,25,65,29,481,1,85,1

%N Let m = A062695(n); a(n) is value of a in decomposition of m defined in Comments.

%C Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

%H G. Kramarz, <a href="http://dx.doi.org/10.1007/BF01451411">All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340.

%H G. Kramarz, <a href="/A003273/a003273.pdf">All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

%Y Cf. A003273, A006991, A062695, A259680-A259687.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 04 2015

%E More terms from _Jinyuan Wang_, Jan 01 2021