% ===analysis
% a^2+b^2 = c^2; c = p-a-b;
% ==> a^2 = (p-a-b)^2-b^2
% ==> a^2 = (p-a)(p-a-2b) = (p-a)^2-2b(p-a)
% ==> p(p-2a) = 2b(p-a) ---(1)
% ==> 2b/p + a/(p-a) = 1
% ==> 2b

% ==> a

function result = euler39()
tic;
maxLen = 3;
for p=120:1000
    curLen = 0;
    for a=3:p/2 % (2)
        if mod(p*(p-2*a),2*(p-a))==0 %(1)
            curLen = curLen+1;
        end
    end
   
    if curLen>maxLen
        maxLen = curLen;
        result = p;
    end
end
toc;
end

% Elapsed time is 0.027793 seconds.
% ans =
%    840