Let a,b,c be integers which are lengths of sides of a triangle, gcd(a,b,c)=1 and all the values (a^{2}+b^{2}-c^{2})/(a+b-c), (b^{2}+c^{2}-a^{2})/(b+c-a), (c^{2}+a^{2}-b^{2})/(c+a-b) are integers as well. Show that (a+b-c)(b+c-a)(c+a-b) or 2(a+b-c)(b+c-a)(c+a-b) is a perfect square.