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n(n+180) is a square.
1

%I #4 Jun 11 2019 19:16:07

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

%N n(n+180) is a square.

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

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

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

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

%t Select[Range[-2200,2200],IntegerQ[Sqrt[#(#+180)]]&] (* _Harvey P. Dale_, Jun 11 2019 *)

%K sign,fini,full

%O 0,1

%A _Harvey P. Dale_, Feb 02 2002