login
A259686
Let m = A062695(n); a(n) is value of c in decomposition of m defined in Comments.
0
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, 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, 161, 7, 1, 1, 1, 1, 7, 3783, 1, 7, 1697, 21, 319, 21, 911, 3, 1
OFFSET
1,2
COMMENTS
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.
LINKS
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 04 2015
EXTENSIONS
More terms from Jinyuan Wang, Jan 01 2021
STATUS
approved