Which of the following claims are true, and which of them are false? If a fact is true you should prove it, if it isn't, find a counterexample. a) Let $a,b,c$ be real numbers such that $ a^{2013} + b^{2013} + c^{2013} = 0 $. Then $ a^{2014} + b^{2014} + c^{2014} = 0 $. b) Let $a,b,c$ be real numbers such that $ a^{2014} + b^{2014} + c^{2014} = 0 $. Then $ a^{2015} + b^{2015} + c^{2015} = 0 $. c) Let $a,b,c$ be real numbers such that $ a^{2013} + b^{2013} + c^{2013} = 0 $ and $ a^{2015} + b^{2015} + c^{2015} = 0 $. Then $ a^{2014} + b^{2014} + c^{2014} = 0 $. Proposed by Matko Ljulj