A067632 n(n+180) is a square.

-2116, -768, -500, -324, -240, -196, -192, -180, 0, 12, 16, 60, 144, 320, 588, 1936

Offset

0,1

Comments

Rewrite it as s^2 - t^2 = 90^2 to see that there are only finitely many solutions.

References

Albert H. Beiler, Recreations in the Theory of Numbers (2d ed. 1966), pp. 296, 317.

Links

Table of n, a(n) for n=0..15.

Example

588 is included because 588 * (588 + 180) = 451584, the square root of which is 672.

Maple

isolve(n*(n+180)=m^2);

Mathematica

Select[Range[-2200, 2200], IntegerQ[Sqrt[#(#+180)]]&] (* Harvey P. Dale, Jun 11 2019 *)

Crossrefs

Sequence in context: A246808 A217439 A365240 * A236446 A077731 A077733

Adjacent sequences: A067629 A067630 A067631 * A067633 A067634 A067635

Keyword

sign,fini,full

Author

Harvey P. Dale, Feb 02 2002

Status

approved