The points P (x₁, y₁) and Q (x₂, y₂) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,
0 x₁, y₁, x₂, y₂ 2.

Given that 0 x₁, y₁, x₂, y₂ 50, how many right triangles can be formed?

+-%cartesian_product
cartesian_product([])->[];
cartesian_product([OneList])->lists:map(fun(X)->[X] end,OneList);
cartesian_product([FirstList|RestLists])->
	Others=cartesian_product(RestLists),
	lists:append(lists:map(fun(Item)-> lists:map(fun(Rest)->[Item|Rest] end, Others) end,FirstList)).

p91()->
	S=lists:seq(0,50),
	Triangles=lists:filter(fun
				 %
				 % Only using the pairs where the angle of the first point (in polar coordinates)
				 % is greater than the second
				 %

				 ([X,Y,X,Y])->false;
				 ([_,_,0,_])->false; % since the first angle must be greater than the second, X2 cannot be 0
				 ([_,0,_,_])->false; % nor can Y1 be 0
				 ([0,A,B,0])->true;
				 ([A,B,A,0])->true;
				 ([0,A,B,A])->true;
				 ([0,A,B,B]) when A == 2*B->true;
				 ([B,B,A,0]) when A == 2*B->true;
				 ([X1,Y1,X2,Y2]) when Y1/X1 =< Y2/X2->false;
				 ([X1,Y1,X2,Y2])->
				 	L1=X1*X1+Y1*Y1,
					L2=X2*X2+Y2*Y2,
					L3=(X1-X2)*(X1-X2)+(Y1-Y2)*(Y1-Y2),
					[L4,L5,L6]=lists:sort([L1,L2,L3]),
					L4+L5==L6
				 end,cartesian_product([S,S,S,S])),
	io:format("~w~n",[length(Triangles)]).