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| Heron at rescue (Posted on 2020-10-23) |
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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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