Let a,b,c be integers which are lengths of sides of a triangle, gcd(a,b,c)=1 and all the values (a²+b²-c²)/(a+b-c), (b²+c²-a²)/(b+c-a), (c²+a²-b²)/(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.

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Posted by Kyle Linel on 2024-10-01 11:18:09