Find integers $f,g,h$ such that $3(f^2+g^2+h^2)=14(fg+gh+hf)$.
You can do it using a computer or by hand.
I tried this problem for ages, got nowhere. Unfortunately I don't know how to program, but I thought it would help a lot here. (Just set up a program to check loads of values until you get one that works?)
I would appreciate any type of solution to this. I only need one (f,g,h) that works.