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

Author

Harvey P. Dale, Feb 02 2002

Keywords

• sign
• fini
• full

Comments

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

Examples

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

References

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

Programs

Maple

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

Mathematica

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