# Number theory ultimatum by Rohith, Anirudh and Arjun!

$$a^{2} + b^{2} + c^{2} = 2(a+b+c+1)$$ and
$$ab+bc+ca = a^{2} + b^{2} + c^{2} - c$$

Let $$a, b, c$$ are positive integers which satisfy the equations above, find $$a + b + c$$.

×