A177760 Values m in solutions of the Thue equation s^2 = m^5+z, sorted along increasing z.

1, 2, 1, 5, 3, 1, 2, 1, 23, 2, 1, 27, 3, 1, 2, 1, 4, 2, 1, 3, 2, 7, 1, 2, 3, 1, 5, 4, 2, 1, 6, 3, 2, 1, 12, 2, 1, 3, 4, 1, 2, 5, 3, 1, 2, 4, 3, 1, 2, 1, 6, 2, 3, 21, 4, 7, 5, 8, 1, 2, 73, 3, 1, 2, 4, 3, 26, 1, 2, 5, 1, 3, 9, 10, 2, 4, 6, 20, 1, 3, 2, 11, 1, 4, 2, 5, 3, 7, 1, 2, 3, 4, 1, 6, 29, 2, 3, 5, 8, 1

Offset: 1

Author

Artur Jasinski, May 13 2010

Keywords

• nonn

Comments

The equation has solutions for the positive z listed in A152412.

A177761 and this sequence here show pairs (s,m) that solve given these z>0. (The case z=0 has infinitely many solutions which are not included here.)

There is no 1-to-1 relation to these z because more than one (s,m) may exist for some z, in case of which all are listed here.

Examples

			(s=59, m=5=a(57), z=356) and (s=182, m=8=a(58), z=356) are solutions associated with z = A152412(57) =356.
(s=20, m=2=a(60), z=368) and (s=45531, m=73=a(61), z=368) are solutions associated with z = A152412(59) =368.
		

Crossrefs

Cf. A152412, A177761.

Formula

A177761(n)^2 = a(n)^5 + A152412(k) for some k>1.

Extensions

Examples and comment on coverage of multiple solutions added - R. J. Mathar, Aug 08 2010