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A067632 n(n+180) is a square. 1
-2116, -768, -500, -324, -240, -196, -192, -180, 0, 12, 16, 60, 144, 320, 588, 1936 (list; graph; refs; listen; history; text; internal format)
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: A107528 A246808 A217439 * A236446 A077731 A077733

Adjacent sequences:  A067629 A067630 A067631 * A067633 A067634 A067635

KEYWORD

sign,fini,full

AUTHOR

Harvey P. Dale, Feb 02 2002

STATUS

approved

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Last modified September 19 12:23 EDT 2021. Contains 347556 sequences. (Running on oeis4.)