<s>[INST] What is the value of $a+b+c$? 
What is the value of $a+b+c$?
if $$a^4+b^4+c^4=32$$
$$a^5+b^5+c^5=186$$
$$a^6+b^6+c^6=803$$

How to approach this kind of problem. Any help.
UPDATE: Thank you all for answers. Now I realize there is no integer solution. But is there any real number solution? I am curious to know.
 [/INST] If $x$ is an integer then $x^4$ and $x^6$ have the same parity. Therefore $a^4+b^4+c^4$ and $a^6+b^6+c^6$ are either both odd or both even.
Therefore there is no solution.
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