A259686 - OEIS

%I #9 Jan 01 2021 04:28:05

%S 1,3,1,17,1,3,1,3,5,1,5,7,7,3,1,1,5,11,1,15,5,7,1,1,1,1,1,7,1,9,15,1,

%T 1,1,1,5,9,7,17,1,97,7,799,11,49,17,1,3,1,1,63,1,1,55,161,3,1,1,1,1,1,

%U 161,7,1,1,1,1,7,3783,1,7,1697,21,319,21,911,3,1

%N Let m = A062695(n); a(n) is value of c 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 1,2

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

%E More terms from _Jinyuan Wang_, Jan 01 2021