Question 67
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 $a^{2014} + b^{2014} + c^{2014} = 0$.
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 $a^{2014} + b^{2014} + c^{2014} = 0$.