Project Euler Problem 9

问题：

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

答案：31875000

Matlab:
%c=1000-a-b
%a^2 + b^2 = (1000-a-b)^2
%b=(1000^2/2-1000*a)/(1000-a) > a
%a can be defined a< 1000-1000/2^.5 = 292
a=0; b=0 c=0;
f=0; %get out from loops
for a=1:292
    for b=a+1:floor((1000-a)/2)
        if a^2+b^2==(1000-a-b)^2
            f=1;
            c=1000-a-b;
            break;
        end
    end
    if f==1
        break;
    end
end

a
b
c
sum=a*b*c

%The answer is 3187500